ImperialQRT Labs

Available projects

Proposals for 2027 entry

These are the PhD projects available for the April and October 2027 intakes. Each has a reference. Select up to three, in order of preference, and quote their references in your project title as set out under Admissions. If you propose your own topic instead, your title ends with (QRT Labs) alone. For more detail on a project, contact its supervisor.

  1. 2027-PP-1

    Economics-Informed Deep Reinforcement Learning for Robust, Explainable Decisions under Uncertainty

    Supervisor: Panos ParpasCo-supervisor: Alexander Michaelides

    Description

    Many problems in economics and finance (saving and investment over a lifetime, asset pricing, market making, monetary and fiscal policy) are sequential decisions under uncertainty.

    Deep reinforcement learning (RL) can learn decision rules for such problems when they are too complex for classical methods, but it ignores what economic theory has already established about the answer: monotonicity and concavity of value and policy functions, budget feasibility, no-arbitrage. Inspired by physics-informed neural networks, this project will develop economics-informed deep RL, in which such restrictions are built into the neural architecture, the training objective and the diagnostics.

    Recent work by the supervisory team shows that neural policies with near-optimal average performance can still behave in economically impossible ways, and that imposing structure removes these errors while improving sample efficiency.

    The project will attempt to provide answers to the following open questions.

    1. Which economic restrictions can be enforced exactly within deep RL, and how do they affect stability, sample efficiency and the compounding of errors over long horizons?
    2. How should policies be trained when parameters are estimated, data are limited and conditions change, drawing on robust RL and the economics of ambiguity?
    3. How can sensitivity analysis, counterfactual explanations and solution-free diagnostics let users change assumptions and see which conclusions survive?

    The methods will first be tested on problems with known solutions, where their accuracy can be measured exactly, and then extended to higher-dimensional and more complicated models for which no solution is known and where the economic restrictions and diagnostics become the only available check. To the extent that they overcome the curse of dimensionality, this opens up richer portfolio choice problems with many assets, income sources and frictions, studied for different actors in the economy (households, corporates, pension and sovereign wealth funds) from both a normative angle (what should an agent do?) and a positive one (does the model explain what agents actually do?). This provides a quantitative laboratory for understanding risk and return trade-offs under realistic uncertainty. The resulting models will be made available through an interface (currently the Model Context Protocol) through which other AI systems can configure, solve and interrogate them while preserving restrictions, communicating uncertainty and flagging when a change invalidates a previous guarantee.

  2. 2027-JB-1

    Generative Pretraining with Population Rewards via Wasserstein Transport

    Supervisor: Joey Bose

    Description

    Generative models are typically pretrained to reproduce an observed data distribution, with reward signals incorporated through subsequent post-training or inference-time steering. However, weak supervision often describes desirable properties of an entire population without providing examples from the distribution we wish to generate. We formulate population-supervised generative learning, in which reference examples and distributional rewards jointly specify the training target through a Wasserstein-regularized variational problem. The resulting target is characterized by a self-consistent transport kernel: reference examples undergo spatial corrections coordinated by shared population feedback. For concave functions of feature expectations, we derive global optimality conditions; for quadratic population discrepancies, we obtain a strongly convex finite-dimensional dual and an explicit optimality certificate. These characterizations motivate a direct mean-field particle algorithm that optimizes the empirical coupling objective without maintaining dual variables, with a descent guarantee under suitable regularity and step-size conditions. An exactly solvable mean-correction problem illustrates how population supervision can revise aggregate statistics while preserving the centered distribution. Finally, we use the evolving particle population as training endpoints for flow matching, incorporating reward information during generative pretraining. The trained model generates independently of the reward oracle, while the Wasserstein cost explicitly determines which departures from the reference population are preferred.

  3. 2027-CT-1

    Scalable, Stable, and Privacy-Preserving Learning Algorithms

    Supervisor: Calvin Tsay

    Description

    Training large models on sensitive or proprietary data requires mitigating noise, adversarial perturbations, and privacy leakage. However, building these guarantees into training usually breaks down at scale. This project studies optimisation algorithms that integrate differential-privacy and stability guarantees directly into the training loop, using structure-exploiting bounding methods that can scale large models. Specifically, building on the group's work on certified training, you'll deploy these certificates in a "search" for scalable, stable, and privacy-preserving learning algorithms. The project advances mathematical optimisation, machine learning, and provable safety.

  4. 2027-CT-2

    Adversarial Robustness in Deep Reinforcement Learning

    Supervisor: Calvin Tsay

    Description

    Reinforcement-learning agents trained on financial markets are often brittle: small, adversarial shifts in market conditions or observations can quickly break a learned strategy. This project develops training methods that make deep RL policies robust under adversarial and out-of-distribution dynamics. We will draw on robust MDPs, safe/constrained RL, and worst-case perturbation analysis. The goal is to stress-test them in realistic market simulators. Building on the group's work in safe and constrained reinforcement learning, as well as in certification, you'll combine RL, robustness methods, and mathematical optimisation.

  5. 2027-FB-1

    Runtime Monitoring and Shielding to Synthesize Safe and Trustworthy RL Controllers

    Supervisor: Francesco Belardinelli

    Description

    Reinforcement Learning has proved to be an effective method to synthesise effective controllers, including for complex tasks.

    However, controllers generated through RL comes with no guarantees about their safety, compliance and trustworthiness, which in high-risk environments might lead to unintended, even harmful, consequences.

    The goal of this project is to (i) build runtime monitors to check compliance of complex stochastic processes with respect to safety, security, trustworthiness requirements; (ii) integrate such monitors into a shielded RL-loop, so as to train controllers that are safe by training.

    Impact

    This PhD project is designed to make the following targeted contributions:

    1. Provide a formalisation of high-risk processes (e.g., industrial, financial, transportation) within the frame of Markov decision processes and games, also accounting for their stochasticity and uncertainty.
    2. Formalise relevant safety and security requirements in logic-based languages amenable to formal verification.
    3. Synthesise monitors automatically from the formal requirements in (2). Then deploy such monitors to verify at runtime the compliance of stochastic processes.
    4. Integrate the monitors into an RL-loop, where the monitors shields against dangerous actions, so as to generate controllers that are safe by training.

    This project will contribute to the monitorability and safety of stochastic, high-risk processes, through the synthesis of controllers that are provably compliant and trustworthy.

    Relevant references by the applicant

    [1] Omar Adalat, Francesco Belardinelli: Expressive Temporal Specifications for Reward Monitoring. AAAI 2026: 19533-19541

    [2] Daniel Donnelly, Francesco Belardinelli: Expressive Reward Synthesis with the Runtime Monitoring Language. PRIMA 2025: 427-434

    [3] Edwin Hamel-De le Court, Francesco Belardinelli, Alexander W. Goodall: Probabilistic Shielding for Safe Reinforcement Learning. AAAI 2025: 16091-16099

  6. 2027-AFR-1

    Algorithmic and Game-Theoretic Aspects of Blockchains and Financial Markets

    Supervisor: Aris Filos-Ratsikas

    Description

    The project aims to study the mathematical foundations that dictate the design of blockchain systems and cryptocurrencies, and more generally related financial markets characterised by volatile assets. The focus will be on the algorithmic aspects of this design (i.e., providing robust and efficient algorithmic solutions), as well as the game-theoretic aspect (i.e., making sure these solutions take the incentives of participants into account, as well as quantify and mitigate their effects).

    An indicative direction is the study of stablecoin design, i.e., cryptocurrencies whose value is pegged to some real-world currency like the USD. The design of stablecoins is a fundamental task faced by many major blockchain companies today, and several different approaches have been proposed (e.g., fiat-backed stablecoins, crypto-back stablecoins, algorithmic stablecoins, etc). Yet, despite all these approaches, there seems to be a striking lack of established theory to back up and aid those designs. Concretely, one would like to systematically study questions of the type: "What is the fundamental principles that guarantee stability?", "Can stability be ensured exclusively via tuning supply and demand via providing the right user incentives?", "What are the appropriate intervention mechanisms that would facilitate those incentives" and, ultimately, "Is it even theoretically possible for a stablecoin to be both stable and long-term sustainable?"

    This direction of the project would aim to develop this theory and back up the theoretical findings with corresponding experiments with real-world data. See for example https://arxiv.org/abs/2602.15981 for a first work in this direction.

    Similar approaches could be applied to other problems in the blockchain/cryptocurrency domain, and more broadly to financial markets which are dictated by the same principles.

  7. 2027-AB-1

    Predictive World Models For Tabular Stock Market Data

    Supervisor: Amir Bar

    Description

    This project explores building a predictive world model for tabular stock market data to simulate future market scenarios and evaluate trading decisions.

    The goal is to learn neural representations of financial data and train a world model that predicts how market and portfolio states evolve under different trading actions.

    We will use this model to plan sequences of trades that optimise risk-adjusted returns under transaction costs and portfolio constraints.

  8. 2027-SD-1

    Neuro-symbolic detection of attacks on enterprise and agentic infrastructure

    Supervisor: Soteris DemetriouCo-supervisor: Francesca Toni

    Description

    Modern computing infrastructure, in finance and beyond, is increasingly operated and extended by AI agents that read, write and execute across many systems. This expands the attack surface in ways that existing detection tools were not designed for: supply-chain compromises can enter through model and dependency repositories, and agents themselves can be turned against their operators by adversarial inputs hidden in the data they process. Statistical detectors struggle to explain their alarms, and rule-based systems struggle to keep up with new behaviours. This project develops neuro-symbolic methods that combine the pattern-recognition strength of modern generative models with the rigour and transparency of symbolic reasoning, with the aim of detecting and localising attacks in system telemetry and agent activity while producing structured, auditable accounts of why a decision was reached. The work also studies how such detectors can be attacked, using adversarial techniques to expose weaknesses and to guide the design of more robust mechanisms. The student will work at the intersection of systems security, explainable AI and adversarial machine learning with access to established public benchmarks. The project is supervised jointly between the APSS (Applications, Systems, and Platforms Security) group and the CLArg (Computational Logic and Argumentation) group and builds on a track record of publications at top security and AI venues.

  9. 2027-SD-2

    Enforcing data-use obligations in AI-driven financial pipelines

    Supervisor: Soteris Demetriou

    Description

    Financial organisations operate under dense contractual and regulatory obligations governing how licensed data may be used, by whom, on which systems, and for how long. As AI agents increasingly orchestrate data ingestion, feature engineering and model training, verifying that these obligations are respected end to end, including in the models trained on the data, is becoming infeasible by manual review or static access control. This project investigates neuro-symbolic techniques for turning natural-language obligations into machine-checkable constraints, monitoring AI-driven data workflows against them, and producing explanations that a compliance officer, vendor or regulator can interrogate. The student will gain expertise in security and privacy, explainable AI and applied machine learning.

  10. 2027-CC-1

    Agents for Program Reasoning

    Supervisor: Cristian Cadar

    Description

    Software development is undergoing a profound transformation, with developers increasingly relying on AI assistants and incorporating AI-generated code. As a result, the core activity of software developers is shifting more and more from writing code to reviewing and validating it.

    However, human-scale code review and validation cannot keep up with the speed and volume of AI-driven development. Therefore, automated software analysis methods—ranging from fuzzing to symbolic execution to formal verification—are becoming critical safeguards in this AI era.

    To remain effective, these methods must scale along multiple dimensions: they must handle larger codebases, keep up with increasingly rapid development cycles, operate across a growing diversity of programming languages and system architectures, and infer and reason about higher-level semantic properties.

    A PhD in this area would focus on addressing these challenges by devising novel agentic technique that combine traditional program analysis techniques and AI-based techniques.

  11. 2027-TB-1

    Topology-Aware Meta-Controllers for Safe and Interpretable Agentic AI

    Supervisor: Tolga Birdal

    Description

    Agentic AI systems increasingly consist not of a single model, but of networks of interacting agents, foundation models, tools, data sources and human decision-makers. Such systems can exhibit collective behaviours that are difficult to infer from any individual component. Agents may form transient coalitions, reinforce erroneous beliefs, propagate failures, develop conflicting internal states, or produce harmful behaviours through interactions that appear benign when examined pairwise. Existing approaches to monitoring and coordinating multi-agent AI largely model these systems either as collections of individual agents or as ordinary graphs. Both representations can miss essential features of agentic systems such as the inherent higher-order interactions.

    This PhD project will investigate whether Topological Deep Learning (TDL) can provide a new mathematical and computational foundation for understanding, controlling and securing agentic AI. The central idea is to represent an evolving agentic system as a higher-order structure, such as a simplicial complex, cell complex, hypergraph or sheaf, in which higher-dimensional cells encode interactions involving groups of agents, tools or information sources. Rather than observing agents independently, this representation would make the organisation of the whole system an explicit object of learning and reasoning.

    The project will develop a topology-aware meta-layer operating above the individual agents. Using topological and geometric representations together with learnable TDL architectures, this layer will seek to identify emerging coordination patterns, inconsistencies and failure modes, as well as quantifying the structural state of the agent network, and, ultimately, intervening when necessary. Possible interventions include modifying communication pathways, isolating compromised components, changing task or information routing, introducing additional verification, or dynamically restructuring teams of agents.

    A core research question is whether topological signatures can reveal emergent failures before they become visible through conventional agent-level metrics. Persistent and dynamic topological summaries, higher-order message passing, Hodge-theoretic representations and sheaf-based consistency models will be investigated as mechanisms for detecting phenomena such as cascading errors, adversarial or compromised agents, unstable feedback loops, groupthink, anomalous coalitions and inconsistent information flows. These representations will also be explored as a route to interpretability: instead of merely assigning a scalar risk score to an agentic system, the meta-layer will expose which interaction structures changed, where inconsistencies arose, and how a failure propagated through the system.

    The project will combine theory and algorithm development with controlled experiments on multi-agent systems based on language models and reinforcement-learning agents. Particular emphasis will be placed on robustness under distribution shift and adversarial behaviour, stability of learned topological representations, scalability to large dynamic agent networks, and intervention-based validation of proposed explanations. An ambitious longer-term goal is to establish conditions under which structural properties of the higher-order interaction network imply guarantees on system-level stability, consistency or containment of failures.

    Financial computing provides a particularly demanding test environment for these ideas. Multi-agent systems used for research, simulation, monitoring, risk analysis or distributed decision support must operate under uncertainty while remaining robust, auditable and resilient to faults. The resulting methods, however, would be broadly applicable to agentic AI systems in other high-stakes domains.

  12. 2027-TB-2

    Learning the Higher-Order Topology of Dynamic Financial Markets

    Supervisor: Tolga Birdal

    Description

    Financial markets are complex adaptive systems in which assets, sectors, institutions and information sources interact across multiple spatial and temporal scales. Most quantitative representations of these dependencies are nevertheless fundamentally pairwise: correlation matrices, covariance networks, graphical models and conventional graph neural networks describe relationships between pairs of entities. Yet many economically meaningful phenomena are intrinsically collective. Market regimes, sector rotations, contagion, coordinated responses to macroeconomic shocks and transient arbitrage relationships may arise through interactions among groups of assets that cannot be adequately reduced to a collection of pairwise dependencies.

    This PhD will develop a new framework for discovering, representing and learning the higher-order structure of dynamic financial markets using Topological Deep Learning (TDL). Rather than assuming that the relevant market network is known in advance, the project will investigate how latent higher-order interactions can be inferred directly from multivariate financial data and represented through structures such as simplicial complexes, cell complexes and hypergraphs. These structures provide a natural mathematical language for encoding interactions among multiple assets simultaneously and for distinguishing genuinely collective effects from combinations of pairwise relationships.

    A central challenge will be that the topology of a market is neither directly observed nor stationary. The project will therefore develop methods for jointly learning market topology and predictive representations through time. Higher-order structures may be inferred from price and return dynamics, volatility, trading activity, cross-asset signals and other multimodal information, with their evolution modelled as a dynamic topological system. Topological Deep Learning architectures will then operate on these learned structures, allowing information to propagate not only between individual assets but across higher-order relationships involving groups, sectors and potentially multiple asset classes.

    The project will investigate whether these representations reveal latent market organisation that is inaccessible to conventional graph-based approaches. For example, topological features may identify the formation or dissolution of tightly interacting groups of assets, changes in the dimensionality or connectivity of market structure, or the emergence of abnormal higher-order dependencies preceding periods of instability. Tools from persistent topology, Hodge theory, higher-order message passing and topological signal processing will be explored alongside learnable neural architectures.

    A major research direction will be dynamic topology discovery. Instead of constructing a market graph using a fixed similarity measure or threshold, the goal will be to learn which interactions are relevant for a downstream task while preserving meaningful structural constraints. This raises fundamental questions at the intersection of machine learning and topology: when is a higher-order relation statistically identifiable? How should topology be regularised across time? Which topological features are stable under noisy observations? And when does modelling interactions beyond pairs provide genuinely new predictive information?

    The learned representations will be evaluated across tasks such as market regime identification, cross-asset forecasting, anomaly and instability detection, risk propagation and out-of-distribution generalisation. Particular attention will be given to periods of structural change, where models based on historical pairwise relationships may fail. Rather than treating these shifts purely as distributional anomalies, the project will investigate whether they can be understood as changes in the topology of the underlying interaction system.

    Interpretability will be a core objective. Because higher-order cells and topological features correspond to explicit structures within the market, the resulting models offer the possibility of explaining predictions through changes in the organisation of interacting assets rather than solely through latent neural representations. The project will investigate methods for attributing model behaviour to particular higher-order interactions and for visualising how learned market structure evolves across regimes.

    The overarching goal is to establish a framework in which financial markets are treated not as fixed graphs but as evolving higher-order systems whose latent topology can be discovered from data. Beyond improving particular predictive tasks, the project aims to answer a more fundamental question: what structure does a machine-learning system discover when it is allowed to learn the geometry and topology of a market rather than having that structure imposed in advance?

    The resulting methods could provide new tools for analysing complex financial systems while contributing more broadly to Topological and Geometric Deep Learning for dynamic, noisy and partially observed environments.

  13. 2027-TB-3

    Learning the Geometry of Financial Markets: Riemannian Machine Learning and Optimisation

    Supervisor: Tolga Birdal

    Description

    Many of the mathematical objects underlying modern quantitative finance are inherently non-Euclidean. Covariance and correlation matrices lie on manifolds of symmetric positive-definite matrices, factor models and dynamic subspaces naturally inhabit Grassmann and Stiefel manifolds, probability distributions admit information-geometric representations, and constrained portfolios, volatility structures and latent market states often possess geometric structure that is lost when they are represented in ordinary Euclidean coordinates.

    At the same time, much of contemporary machine learning and numerical optimisation treats these objects as unconstrained vectors in a flat parameter space. This can lead to inefficient optimisation, unstable learning, poor extrapolation and models that fail to respect the intrinsic structure of the quantities being learned.

    This PhD will investigate a different paradigm: can the geometry of financial models and financial data be exploited, and in some cases learned—to obtain more efficient, stable and interpretable machine-learning and optimisation methods?

    The project will develop methods at the intersection of Riemannian geometry, machine learning, optimisation and quantitative finance. A central focus will be the design of geometry-aware learning algorithms in which optimisation takes place directly on the appropriate manifold rather than through an unconstrained Euclidean parameterisation. Candidate geometries include the manifold of symmetric positive-definite matrices, Grassmann and Stiefel manifolds, product manifolds arising from structured financial models, and information-geometric spaces of probability distributions.

    One research direction will investigate Riemannian optimisation for dynamic covariance, factor and risk models. Financial dependence structures are high-dimensional, noisy and time-varying, yet their mathematical representations possess strong geometric constraints. The project will study whether geodesic interpolation, intrinsic regularisation, Riemannian gradient methods and manifold-valued dynamical models can improve the estimation and tracking of these structures, particularly during periods of regime change or market stress.

    A second direction will explore Riemannian machine learning for financial prediction and representation learning. Instead of first embedding structured financial objects into Euclidean space, models could operate directly on manifold-valued inputs or latent states. This may include geometry-aware neural architectures, Riemannian recurrent or state-space models, and manifold-valued latent representations for evolving market states. Applications could include regime identification, volatility and risk forecasting, cross-asset modelling and anomaly detection.

    A particularly ambitious component of the project will ask whether the relevant latent geometry itself can be learned from data. Classical Riemannian methods assume that a metric is specified in advance. In a financial system, however, the geometry that best captures economically meaningful similarity or sensitivity may change through time. The project will therefore investigate adaptive or learned Riemannian metrics that reflect the local structure of market dynamics and simultaneously improve downstream optimisation.

    This creates a close connection between learning and optimisation, determining which perturbations are small, which directions are important, and how optimisation trajectories evolve. The project will investigate whether such learned geometries can act as task-dependent preconditioners, producing faster and more stable optimisation while retaining an interpretable relationship to financial structure.

    The theoretical component will study questions of convergence, stability and generalisation on curved parameter spaces. This may include analysis of Riemannian stochastic gradient methods, natural-gradient-like algorithms, geodesic convexity, adaptive metrics, and the interaction between manifold curvature and the conditioning of high-dimensional financial optimisation problems. Where appropriate, the project will seek guarantees concerning convergence rates, robustness to noisy observations and stability under changes in market regime.

    Various financial applications will provide demanding test cases in which structural constraints and non-stationarity are unavoidable. Potential problems include dynamic covariance estimation, portfolio and risk optimisation, latent factor tracking, volatility modelling, market-regime identification and uncertainty quantification. The objective is not simply to apply existing manifold algorithms to finance, but to use financial problems to motivate new methods in Riemannian machine learning and optimisation.

    The broader goal of the PhD is to establish a principled framework for geometry-aware learning in dynamic, high-dimensional systems, addressing a fundamental question: when the objects being learned are intrinsically curved, how much can be gained by allowing the learning and optimisation algorithms to respect—and ultimately discover—that geometry?

  14. 2027-AD-1

    Formally Verified LLM Inference

    Supervisor: Alastair DonaldsonCo-supervisor: Marios Kogias

    Description

    LLM inference engines are critical infrastructure on which societies around the world depend. Cyber attacks on LLM infrastructure have the potential to deny access to critical services, compromise privacy and isolation between tenants in data centres, and form the basis of remote execution attacks. This PhD project will focus on the design of secure-by-construction LLM inference engines using formal methods, through the Lean proof assistant. It would be ideal for a student who is interested in (a) how inference works at the systems level (including how to work with highly optimised GPU kernels and multi GPU setups in a distributed environment), (b) using formal methods at scale, and (c) leveraging generative AI to apply proof assistants effectively in this setting.

  15. 2027-RB-1

    Quantum Computing for Learning Under Uncertainty

    Supervisor: Roberto Bondesan

    Description

    Can quantum computers find better solutions in the complex optimisation landscapes that arise when learning from noisy data? This PhD project will explore how quantum dynamics can navigate nonconvex objectives, building on emerging connections between quantum mechanics, stochastic processes, and optimisation. A central challenge is to understand when quantum advantages survive the uncertainty, interactions, and computational costs encountered in realistic learning problems. The research will combine mathematical analysis, quantum algorithm design, and numerical experiments, with potential applications to financial model calibration and nonlinear time-series learning within QRT Labs. By comparing quantum approaches with powerful classical methods, the project aims to establish when quantum computation can deliver reliable solutions more efficiently and how to design algorithms that exploit those opportunities. It offers an exciting opportunity for students interested in quantum computing, applied mathematics, and machine learning to work at the interface of fundamental theory and practical challenges.

  16. 2027-HF-1

    Privacy-Aware Heterogeneous Edge-to-Core System for Financial Applications

    Supervisor: Hongxiang Fan

    Description

    The rapid adoption of AI in financial computing is increasing the demand for more capable models, while also placing greater pressure on latency, scalability, and the secure handling of sensitive data. Financial workloads are becoming increasingly heterogeneous, often requiring different forms of market, transaction, and institutional data to be analysed together rather than by a single model or computing environment. This project therefore investigates how machine learning can be co-designed with distributed systems to support scalable, efficient, and privacy-aware heterogeneous financial computing.

    Many financial applications require information from multiple data sources and computational environments to be combined in order to support timely and accurate decision-making. Examples include market analysis, risk assessment, transaction analytics, and other data-intensive financial services. Processing such workloads across local and central systems creates an important trade-off: filtering or compressing data can reduce communication and computational overhead, but may also remove information that is important for downstream analysis. Transmitting detailed data to central systems can increase resource consumption and expose sensitive financial or proprietary information. This challenge becomes even more prominent with large language models (LLMs), whose heavy computational and memory requirements and large input contexts can significantly amplify communication costs and privacy risks in distributed deployments. This raises the question of how specialised models should be distributed across the computing hierarchy and what information should be exchanged between them.

    Building on our prior work on efficient multi-model inference, such as edge infrastracture for LLM test-time scaling, this project aims to develop a privacy-aware heterogeneous edge-to-core framework for financial applications. The framework will determine where specialised models should execute and how intermediate information should be exchanged between local and central components. It will explore adaptive mechanisms for retaining task-relevant information while reducing unnecessary transmission and exposure of sensitive data. Its effectiveness will be assessed against local-only, centralised, and fixed-partition systems, considering both application-level performance and system-level costs such as latency, communication overhead, resource utilisation, scalability, and information leakage.

  17. 2027-DP-1

    Safe Learning and Control Out of Distribution

    Supervisor: Dario Paccagnan

    Description

    Modern AI and control systems are trained on finite data, yet they are deployed in environments that rarely behave exactly like the data used for training. Distribution shifts may arise from changing operating conditions, modelling errors, sensor biases, new environments, or interactions between a controller and the system it controls.

    This PhD will develop new methods for safe learning and control under distribution shift, with the goal of providing rigorous guarantees on the behaviour of learning-enabled systems when deployment differs from training. The project will combine ideas from machine learning, optimisation, control theory, statistical learning and formal verification.

    Research questions will include how to certify safety from finite data, how to exploit physical and temporal structure in distribution shifts, and how to design controllers that remain reliable beyond the observed training distribution. The work will span fundamental theory, new algorithms, and applications to learning-enabled dynamical systems.

    The project is particularly suited to students interested in the mathematical foundations of reliable AI, safe machine learning, optimisation, or data-driven control.

  18. 2027-MK-1

    Operating System Support for Emerging Optical Networking

    Supervisor: Marios Kogias

    Description

    Datacenter networks have seen a tremendous advancement over the past 20 years with Cloud computing, AI workloads, and high-performance computing (HPC) being the main driving forces. Despite already reaching speeds of 800Gbps per port and multiple Pbps of bisection bandwidth, emerging applications such as AI training and agentic workloads require more and more bandwidth, while having a substantially different workload profile with more predictable and large flows.

    Unfortunately, the majority of datacenter networking infrastructure depends on electrical packet-switched networks which are are increasingly constrained in terms of scalability, power consumption, and bandwidth capacity. At the same time, emerging optical networking technologies, and specifically optical circuit switching, offer unprecedented bandwidth and energy efficiency, and optical switches have a much lower operational carbon footprint. Recent research prototypes such as Helios, RotorNet, and Sirius demonstrate that optical switching technologies can provide extremely high-capacity interconnects with microsecond or even nanosecond switching times. In parallel, hyperscale operators are beginning to integrate optical circuit switching into production networks, as illustrated by Google’s evolving datacenter network architecture.

    Despite these advances, existing operating systems and distributed systems software remain fundamentally designed for electrical packet-switched networks. Operating systems assume they can transmit packets over the network at any point in time. Yet, optical fabrics operate using circuit-based communication and dynamically reconfigurable topologies. These characteristics introduce new challenges for existing hardware and software starting from the network interface card and its capabilities all the way to resource management, application scheduling, and communication abstractions. As a result, current systems software and hardware cannot effectively exploit the unique capabilities of optical networking hardware.

    This project proposes to develop operating system support for emerging optical networking technologies. The central vision is to make optical connectivity a first-class resource within the operating system and cluster software stack, enabling applications to dynamically exploit high-bandwidth optical circuits. The project will pursue three main research objectives. First, it will focus on the NIC hardware and revisit it specifically for the case of reconfigurable network. Second it will design operating system abstractions that expose optical connectivity to applications and system software. Kernel-level interfaces and user-space APIs will enable applications to request high-bandwidth optical paths when needed. Third, it will will develop runtime mechanisms for adaptive optical network reconfiguration, enabling the system to decide when circuit reconfiguration is beneficial based on communication patterns and workload dynamics.

  19. 2027-MK-2

    Confidential Computing for Agentic Workloads

    Supervisor: Marios Kogias

    Description

    Confidential computing protects data during a computation, providing the necessary complement in the cloud to existing protections for data at rest and in transit. The ecosystem is maturing rapidly: hardware vendors ship Trusted Execution Environments (TEEs), cloud providers offer confidential-computing services built on them, and a growing body of academic work extends them further. The trust model underpinning TEEs, however, was conceived for software that is static, auditable, fully measured at deployment, and functionally trusted to handle confidential data without leakage --- assumptions that no longer hold for emerging workloads, particularly agentic applications that generate and execute code at runtime.

    Today's TEEs adopt a myopic view of confidentiality, providing only half of what is needed. The first half is covered by hardware: it protects a TEE's exclusive resources, above all its private memory, from higher-privilege software, and attests a launch-time measurement of the TEE's initial code and configuration. The other half is not: a TEE's confidentiality also depends on its shared channels. These include shared memory, communication buffers, and control transfers to untrusted software. Existing TEE architectures neither constrain what may flow across these channels nor attest any policy that bounds them.

    This blind spot forces a fundamental conflation of confidentiality and trust: the only way to guarantee confidentiality is to trust all TEE-resident code that accesses shared channels to prevent data leakage. In this model, every such component becomes part of the Trusted Computing Base (TCB) for confidentiality. For this model to work, the TCB must be stable enough for tenants to know which measurement to expect at attestation time, small enough to audit, and functionally trusted to use shared channels without leakage.

    That trust is brittle: shared channels are broad, unconstrained, and neither measured nor bounded by attestation. Code that can access them is rarely stable: modern software stacks evolve through frequent updates and dependencies that may change independently. Nor is it small enough to audit: these stacks combine complex low-level systems code (e.g., virtio drivers) with many libraries and elaborate dependency patterns, making comprehensive audits difficult. Most importantly, correctness remains a functional assumption, so a single bug or misuse in code that accesses shared channels is enough to break confidentiality.

    To make matters worse, modern workloads may not even expose the relevant code at attestation time. Agentic applications make this problem structural: the logic that handles confidential data may be generated or selected at runtime in response to LLM outputs and external tool calls, rather than being static, auditable, and fully present at deployment. The problem extends beyond agentic systems: cloud workloads increasingly run as CVM pipelines operated by separate parties, with proprietary code, asymmetric trust, and limited willingness or ability to audit one another. In short, today's TEEs offer confidentiality only at the price of a trust assumption modern workloads cannot pay.

    The purpose of this project is to study emerging complex cloud and agentic applications that comprise of multiple distrustful components and design the future of TEE architectures, i.e., an extension to existing TEEs that will allow attestable and trusted workflows out of distrustful components. To do so, we will work on existing RISC ISAs, and specifically ARM CCA, that allow for extensibility and design an architecture that achieves so through a combination of low-level engineering, Domain-Specific-Language design, and lightweight formal methods.

  20. 2027-EN-1

    Microstructural Foundations of Passive Impact and Cross-Impact

    Supervisor: Eyal Neuman

    Description

    This research will investigate how passive liquidity provision influences prices within and across assets. Building on a recently developed mesoscopic execution framework, it will examine how limit-order placement, cancellation, and execution generate passive price impact through order-flow imbalance and liquidity dynamics. The aim is to derive tractable models of passive impact and cross-impact, distinguishing trading-induced effects from adverse selection and common information. These models will be applied to optimal execution, portfolio optimisation, and market making, accounting for uncertain fills, inventory risk, and endogenous trading costs.

  21. 2027-EN-2

    Language Models for Market Microstructure

    Supervisor: Eyal NeumanCo-supervisor: Panos Parpas

    Description

    This research will investigate whether language models can improve predictions of execution outcomes in limit order book and over-the-counter markets. It will develop finance-specific models that process order-book events and OTC request-for-quote records alongside financial news and macroeconomic announcements. The main prediction tasks will be limit-order fill probabilities and client acceptance of dealer quotes. The project will test whether textual information adds predictive value beyond numerical market data, and compare small specialised language models with larger models and conventional forecasting methods. Evaluation on later, unseen data will assess predictive accuracy, computational cost, and the usefulness of these forecasts for execution and market-making decisions.

  22. 2027-EN-3

    Quantum Advantage in Trading and Tail Risk

    Supervisor: Eyal Neuman

    Description

    This research will investigate the potential for quantum advantage in portfolio choice, optimal execution, and rare-event sampling. It will develop quantum sampling methods to accelerate the evaluation of candidate trading strategies. Particular attention will be given to optimisation with tail-risk constraints or risk-sensitive objectives, where rare outcomes can materially change the preferred strategy. The central objective is to establish when quantum methods outperform advanced classical algorithms at a prescribed level of solution accuracy. The analysis will account for numerical errors, quantum state preparation, and the cost of producing usable trading decisions. It will develop Schrödinger bridge methods for generating market scenarios, quantum Gibbs sampling, estimation procedures using the quantum Fourier transform, and quantum optimisation algorithms to evaluate and improve candidate trading strategies.

  23. 2027-RP-1

    Multi-Agent World Action Models for Complex Systems

    Supervisor: Rolandos Potamias

    Description

    World Models have proven to be a valuable paradigm capturing the dynamics of complex environments that require accurate prediction of future states and high-level planning of actions. By enabling learned latent representations of continuous time, these architectures allow autonomous agents to imagine and predict future dynamical states before committing to a course of action.

    While previous methods have shown promise, they are limited in that they are either non-interactive or single-agent: most approaches treat the environment as a passive entity with no ability to be influenced by an agent's decisions, or are incapable of capturing the interplay between multiple independent entities. In contrast, in real-world, many environments exist which are interactive and composed of multiple independent actors, such as the dynamics of physical spatial scenes, financial markets, or other high-frequency interaction graphs.

    This project aims to explore Multi-Agent World Action models (MA-WAMs) as a flexible new generative paradigm which couples the latent interactions of an environment to the coordinated actions of multiple autonomous entities. By combining continuous latent world models with continuous multi-agent games, these architectures allow agents to reason counterfactually about how their own actions, and the coordinated or competitive actions of other entities will evolve into the future.

  24. 2027-FB-2

    Formal Methods for Probabilistic Safe Reinforcement Learning: Improving Safety of RL algorithms with Shielding

    Supervisor: Francesco Belardinelli

    Description

    Reinforcement Learning (RL) [17] aims to optimise the behaviour of an agent in an unknown environment.

    In real-life scenarios, however, safety, either for the agent or for other humans, is critical.

    In recent years, Safe RL has thus been developed, in which the aim is to optimize the behaviour of an agent under one or several safety constraints.

    In particular, one of the core problems of Safe RL is solving CMDPs (Constrained Markov Decision Process) [13], where the agent must obtain as much reward as possible while keeping its cost under a threshold d.

    CMDPs are versatile and model many practical applications of interest, including e.g. smart utility grids, robotics, or trading.

    However, most of the existing learning algorithms lack formal safety guarantees (like e.g. Lagrangian-types [11], CPO [12], or FOCOPs [18]) or too conservative (like e.g. Saute algorithms [16] or ProSH [15]), i.e. either lead to a high reward but at a cost that violates the cost threshold d, or to a cost that is in practice under the cost threshold d but with a much lower reward.

    The project aims to construct a new learning algorithm for CMDPs by applying a shielding mechanism [14] to transform unsafe algorithms that yield high rewards into algorithms that are provably and practically safe.

    The student will design a new algorithm by applying Probabilistic Shielding [14] to Lagrangian-type algorithms for CMDPs [11].

    The main idea of Lagrangian-type algorithms is to transform the constrained optimization problem of optimizing the agent while abiding by the cost constraint into an unconstrained optimization problem by replacing the original agent’s reward by a linear combination of its reward and cost.

    While Lagrangian-type algorithm provably converge, in theory, to the sought-after solution, they suffer in practice from “oscillating” behaviours where the cost forever oscillates around the threshold d, leading to a lack of stability and a large amount safety violations.

    Probabilistic Shielding should provide a solution this well-known issue by modifying the agent’s actions so that it always remain safe.

    The student will implement the new algorithm and benchmark it with safety-gym [11], thereby expanding the MASA-Safe-RL library (https://github.com/sacktock/MASA-Safe-RL).

    Primary objectives

    1. Algorithm Development with Formal Guarantees: Develop a tabular reinforcement learning algorithm with formal guarantees (e.g., PAC guarantees, convergence, bound on constraint violations) under a chosen class of probabilistic safety constraints (e.g., probabilistic reachability, reach-avoid, LTL, or PCTL).
    2. Integration into MASA-Safe-RL: Implement the proposed algorithm within the MASA-Safe-RL library in a manner consistent with its existing abstractions and design.
    3. Empirical Evaluation: Perform an extensive experimental evaluation on benchmark environments, comparing performance, safety satisfaction, and conservatism against relevant baselines.

    Advanced Objectives

    1. Extension to Deep Reinforcement Learning: Extend the proposed probabilistic safety framework to deep RL settings using function approximation (e.g., DQN, PPO).
    2. Neural Representations and Scalability: Investigate neural representations of safety-related quantities (safety critic) and evaluate scalability to higher-dimensional or continuous environments.

    Suitable skills/background requirements

    To complete this project successfully, the student should have a background in at least one of Reinforcement Learning (incl. deep RL) or Formal Methods, with an interest in learning more about the other subject. Good programming skills are also essential.

    Representative references

    [1] Fu, Jie, and Ufuk Topcu. "Probably approximately correct MDP learning and control with temporal logic constraints." arXiv preprint arXiv:1404.7073 (2014).

    [2] Hsu, Kai-Chieh, Haimin Hu, and Jaime F. Fisac. "The safety filter: A unified view of safety-critical control in autonomous systems." Annual Review of Control, Robotics, and Autonomous Systems 7 (2023).

    [3] Belardinelli, Francesco, and Alexander W. Goodall. "Probabilistic Shielding for Safe Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 39. No. 15. 2025.

    [4] Voloshin, Cameron, et al. "Policy optimization with linear temporal logic constraints." Advances in Neural Information Processing Systems 35 (2022): 17690-17702.

    [5] Voloshin, Cameron, Abhinav Verma, and Yisong Yue. "Eventual discounting temporal logic counterfactual experience replay." International Conference on Machine Learning. PMLR, 2023.

    [6] Shah, Ameesh, et al. "LTL-Constrained Policy Optimization with Cycle Experience Replay." arXiv preprint arXiv:2404.11578 (2024).

    [11] Joshua Achiam and Dario Amodei. Benchmarking safe exploration in deep reinforcement learning. 2019.

    [12] Joshua Achiam, David Held, Aviv Tamar, and Pieter Abbeel. Constrained policy optimization. In Doina Precup and Yee Whye Teh, editors, Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6-11 August 2017, volume 70 of Proceedings of Machine Learning Research, pages 22–31. PMLR, 2017.

    [13] Eitan Altman. Constrained markov decision processes. 1999.

    [14] Edwin Hamel-De le Court, Francesco Belardinelli, and Alexander W. Goodall. Probabilistic shielding for safe reinforcement learning. In Toby Walsh, Julie Shah, and Zico Kolter, editors, AAAI-25, Sponsored by the Association for the Advancement of Artificial Intelligence, February 25 - March 4, 2025, Philadelphia, PA, USA, pages 16091–16099. AAAI Press, 2025.

    [15] Edwin Hamel-De le Court, Gaspard Ohlmann, and Francesco Belardinelli. Prosh: Probabilistic shielding for model-free reinforcement learning. CoRR,abs/2510.15720, 2025.

    [16] Aivar Sootla, Alexander I. Cowen-Rivers, Taher Jafferjee, Ziyan Wang, David Henry Mguni, Jun Wang, and Haitham Ammar. Saute RL: almost surely safe reinforcement learning using state augmentation. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesv´ari, Gang Niu, and Sivan Sabato, editors, International Conference on Machine Learning, ICML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pages 20423–20443. PMLR, 2022.

    [17] Richard S. Sutton and Andrew G. Barto. Reinforcement Learning: An Introduction. A Bradford Book, Cambridge, MA, USA, 2018.

    [18] Yiming Zhang, Quan Vuong, and Keith W. Ross. First order optimization in policy space for constrained deep reinforcement learning. CoRR,abs/2002.06506, 2020.

  25. 2027-FB-3

    Reasoning About the Strategic Abilities of Autonomous Agents in Partially Observable Stochastic Games

    Supervisor: Francesco Belardinelli

    Description

    This project aims at pushing forward the specification and verification of strategic abilities of autonomous agents in stochastic games with partial observability.

    Our key objective is to extend the ATL*AS model checker currently developed at the Formal Methods for AI lab (https://fmailab.doc.ic.ac.uk/), led by Dr Francesco Belardinelli.

    In particular, we want to extend ATL*AS to partially observable stochastic games, which feature prominently in AI applications.

    Such an extension requires both theoretical advances in formal verification and technological contributions in model checking technologies.

    The specification and verification of strategic abilities of autonomous agents in multi-agent systems (MAS) has been a thriving area of research in the past 30 years.

    In several multi-agent applications we are not only interested in reaching some goals or avoiding unsafe states, but we also want to synthesize strategies, policies needed by agents to bring about those goals: the autonomous car needs to have a strategy/plan/policy to reach destination, while avoiding crashing into other vehicles.

    Alternating-time Temporal Logic (ATL) is a logic-based language suitable to express this kind of properties. Its key feature is to extend the linear-time temporal logic LTL with strategy operator << A >>, which intuitively represents the fact that coalition A of agents has a strategy to achieve some goal. As such, we can express the property of the autonomous car above as << car >> (Eventually "destination" & Always not "crash").

    In [Garcia and Belardinelli, 2026], we developed ATL*AS, a model checking tool to check specifications expressed in ATL on multi-agent systems in an automated way, however, with one key restriction: we assumed that agents have perfect information about their environment. But in MAS, agents can typically observe only a part of their environment, possibly because of limitations in sensing or in computational resources.

    The goal of this project is to extend ATL*AS to support agents with imperfect information/partial observability about their environment. This extension raises a number of questions both theoretical (increased computational complexity) and practical (implementation issues). In particular, we anticipate to explore neural model checking [Giacobbe et al., 2024] to improve the performance of the verification step.

    Your contribution will be the development of a model checking tool for multi-agent systems wrt properties expressed in ATL under the assumption of imperfect information/partial observability, possibly by leveraging on neural model checking.

    You will then evaluate the performance of the tool in several multi-agent scenarios of interest, particularly from the literature on security.

    Suitable skills/background requirements

    To complete this project successfully it is required a background in formal methods, possibly verification by model checking. Also, the student should have an interest in multi-agent system, strategic reasoning, (partially observable) stochastic games, logic-based formalisms including temporal logics. Good programming skills (C/C++) are also required.

    Representative references

    [Alur et al., 2002] R. Alur, T. Henzinger, and O. Kupferman. Alternating-time temporal logic. Journal of the ACM, 49(5):672–713, 2002.

    [Belardinelli et al., 2018] F. Belardinelli, A. Lomuscio, A. Murano, S. Rubin: Alternating-time Temporal Logic on Finite Traces. IJCAI 2018: 77-83

    [Mogavero et al., 2014] F. Mogavero, A. Murano, G. Perelli, and M. Y. Vardi. Reasoning about strategies: On the model-checking problem. ACM Transactions on Computational Logic, 15(4):34:1–34:47, 2014.

    [Harel and Pnueli, 1985] D. Harel and A. Pnueli. On the development of reactive systems. In Logics and models of concurrent systems, pages 477–498. Springer, 1985.

    [Jennings et al., 2001] N. R. Jennings, P. Faratin, A. Lomuscio, S. Parsons, M. Wooldridge, and C. Sierra. Automated negotiation: prospects, methods and challenges. Group Decision and Negotiation, 10(2):199–215, 2001.

    [Pesic et al., 2010] M. Pesic, D. Bosnacki, and W. M. P. ravan der Aalst. Enacting declarative languages using LTL: avoiding errors and improving performance. In SPIN, LNCS 6349, pages 146–161, 2010.

    [Geffner and Bonet, 2013] H. Geffner and B. Bonet. A Concise Introduction to Models and Methods for Automated Planning. Morgan & Claypool Publishers, 2013.

    [Tsai et al., 2014] M.-H. Tsai, S. Fogarty, M. Y. Vardi, and Y.-K. Tsay. State of Büchi complementation. Logical Methods in Computer Science, 10(4), 2014.

    [Giacobbe et al., 2024] https://arxiv.org/abs/2410.23790

    [Garcia and Belardinelli, 2026] S. Garcia de Blas Garcia-Alcalde, F. Belardinelli: ATL*AS: An Automata-Theoretic Approach and Tool for the Verification of Strategic Abilities in Multi-Agent Systems. AAMAS 2026.

    [Belardinelli et al. 2023] Francesco Belardinelli, Wojciech Jamroga, Munyque Mittelmann, Aniello Murano: Strategic Abilities of Forgetful Agents in Stochastic Environments. KR 2023: 726-731

    [Belardinelli et al. 2024] Francesco Belardinelli, Wojtek Jamroga, Munyque Mittelmann, Aniello Murano: Verification of Stochastic Multi-Agent Systems with Forgetful Strategies. AAMAS 2024: 160-169

  26. 2027-CPB-1

    Understanding Randomized Exploration in Modern Reinforcement Learning

    Supervisor: Ciara Pike-Burke

    Description

    Randomized exploration is a central ingredient in modern reinforcement learning and sequential decision-making algorithms, underpinning widely used approaches such as softmax policy gradient methods and posterior-sampling. While these methods often perform well empirically in large-scale environments, the theoretical understanding of their effectiveness is still incomplete.

    This project will develop a rigorous mathematical understanding of randomized exploration by studying when and why such methods learn efficiently. The focus will be on identifying structural conditions on the optimization procedure or environment under which randomized strategies provably balance exploration and exploitation effectively. We will draw on tools from optimization, probability, and statistical machine learning to derive finite-sample guarantees and characterise the performance of this class of practically relevant algorithms.

    The project sits at the intersection of reinforcement learning, stochastic optimization, and learning theory, and will contribute to the broader goal of improving the reliability and scalability of decision-making methods in complex high-dimensional systems.

  27. 2027-WL-1

    Agent-based Learning for Interpretable Financial Risk Management

    Supervisor: Wayne LukCo-supervisor: Ce Guo

    Description

    Agent-based modeling is a technique for modeling complex systems to improve our understanding of system behaviours. They have been used in financial applications to simulate how customers, regulators, corporations, banks, or investors interact with one other, and how that interaction could cause specific events to happen to them and to financial markets. There is growing interest in adopting agent-based modelling for financial services [1]. We have been working with the Bank of England on updating and accelerating an agent-based model for the UK housing market [2]. The proposed research will build on this collaboration to manage national-level financial risks such as crashes.

    This project concerns improving agent-based modelling for financial risk management, by combining and extending three of our recent advances. First, the use of surrogate modelling for calibrating agent-based simulation of financial crashes [3]. Second, extension of interpretable methods to target risk management strategies [4]. Third, adoption of high-performance digital twin capabilities to accelerate interpretable agent-based financial risk analysis [5]. The results could help address Bank of England's concerns about managing potential financial instabilities [6].

    References

    [1] Simudyne, A Complete Guide to Agent-Based Modeling for Financial Services, https://simudyne.com/wp-content/uploads/2019/08/A4-Guide-to-ABM-FINAL-5.pdf

    [2] Bank of England Working Paper, Heterogeneous effects and spillovers of macroprudential policy in model of uk housing market, 2022. https://www.bankofengland.co.uk/working-paper/2022/heterogeneous-effects-and-spillovers-of-macroprudential-policy-in-model-of-uk-housing-market

    [3] K. Gao et al., High-Frequency Financial Market Simulation and Flash Crash Scenarios Analysis: An Agent-Based Modelling Approach. Journal of Artificial Societies and Social Simulation 27 (2) 8, 2024. https://www.jasss.org/27/2/8.html

    [4] L. Faloughi, C. Guo and W. Luk, ProtoHedge: Interpretable Hedging with Market Prototypes. ICAIF, pp. 202-210, 2025. (Best Student Paper Award)

    [5] A.T. L. Leung, C. Guo and Wayne Luk, FABS: An Extensible and High-Performance Digital Twin Framework of AI-Driven Financial Systems. ICAIF, 27-34, 2025.

    [6] BBC News, Stock markets are too high and set to fall, says Bank of England deputy. https://www.bbc.co.uk/news/articles/c75kp1y43lgo

  28. 2027-NK-1

    The Morse–Witten Machine: Escaping Local Optima in Recursive Program Search

    Supervisor: Nikolas KantasCo-supervisors: Panos Parpas, Greg Pavliotis

    Description

    This PhD project will develop and evaluate the Morse–Witten Machine, a framework for recursive self-improvement whose search domain is the space of all possible programs expressible in a chosen programming language. Rather than optimising over a prescribed continuous space, such as a Riemannian manifold, the project will search over executable programs, including those implementing the agent’s own search and improvement procedures. Building on Witten-Laplacian methods for locating index-1 saddle points [1], it will construct tractable continuous representations of subsets of program space and test whether their transition geometry helps identify useful program modifications. The theoretical programme will analyse convergence and sensitivity to evaluation noise for the resulting surrogate search problems under explicit assumptions. A practical implementation will combine interacting-particle search, local saddle refinement and language-model-generated proposals, with candidate programs assessed through execution under defined resource limits. The recursive component will permit modifications to the procedures used to generate and select subsequent candidates. Evaluation will use common tasks, fixed external assessment criteria and matched computational budgets, with ablation studies measuring the contribution of geometric guidance. Comparisons will include evolutionary and self-modifying search informed by AlphaEvolve [2], the Darwin Gödel Machine [3] and the Red Queen Gödel Machine [4], alongside GEPA [6] and Agentic Context Engineering [7]. Financial applications will focus on generating and testing interpretable hypotheses about stock returns around earnings announcements, following the evaluation setting in [5]. Experiments will use information available at each decision date, prospective evaluation and independent replication to assess explanatory performance and robustness while limiting information leakage and adaptive overfitting. The project will deliver a mathematical analysis, a reproducible implementation and empirical evidence on whether saddle-guided exploration improves the quality or computational efficiency of program search and automated financial research.

    References

    [1] Lelièvre, T. and Parpas, P. (2024). Using Witten Laplacians to Locate Index-1 Saddle Points. SIAM Journal on Scientific Computing, 46(2), A770–A797. DOI: 10.1137/22M1541964.

    [2] Novikov, A. et al. (2025). AlphaEvolve: A Coding Agent for Scientific and Algorithmic Discovery. Google DeepMind white paper. arXiv:2506.13131.

    [3] Zhang, J., Hu, S., Lu, C., Lange, R. and Clune, J. (2026). Darwin Gödel Machine: Open-Ended Evolution of Self-Improving Agents. International Conference on Learning Representations (ICLR 2026). arXiv:2505.22954.

    [4] Iacob, A. et al. (2026). The Red Queen Gödel Machine: Co-Evolving Agents and Their Evaluators. Preprint. arXiv:2606.26294.

    [5] Koijen, R. S. J. and Levy, B. (2026). Assessing the Benefits of Optimized Agentic AI Systems for Asset Pricing. NBER Working Paper No. 35431, July 2026. DOI: 10.3386/w35431.

    [6] Agrawal, L. A. et al. (2026). GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning. International Conference on Learning Representations (ICLR 2026). arXiv:2507.19457.

    [7] Zhang, Q. et al. (2026). Agentic Context Engineering: Evolving Contexts for Self-Improving Language Models. International Conference on Learning Representations (ICLR 2026). arXiv:2510.04618.