Leo Ardon

Leo Ardon, Jared Vann, Deepeka Garg et al.

Agent based modelling (ABM) is a computational approach to modelling complex systems by specifying the behaviour of autonomous decision-making components or agents in the system and allowing the system dynamics to emerge from their interactions. Recent advances in the field of Multi-agent reinforcement learning (MARL) have made it feasible to study the equilibrium of complex environments where multiple agents learn simultaneously. However, most ABM frameworks are not RL-native, in that they do not offer concepts and interfaces that are compatible with the use of MARL to learn agent behaviours. In this paper, we introduce a new open-source framework, Phantom, to bridge the gap between ABM and MARL. Phantom is an RL-driven framework for agent-based modelling of complex multi-agent systems including, but not limited to economic systems and markets. The framework aims to provide the tools to simplify the ABM specification in a MARL-compatible way - including features to encode dynamic partial observability, agent utility functions, heterogeneity in agent preferences or types, and constraints on the order in which agents can act (e.g. Stackelberg games, or more complex turn-taking environments). In this paper, we present these features, their design rationale and present two new environments leveraging the framework.

Harish Karthikeyan, Yue Guo, Leo de Castro et al.

As AI agents increasingly operate in complex environments, ensuring reliable, context-aware privacy is critical for regulatory compliance. Traditional access controls are insufficient because privacy risks often arise after access is granted; agents may inadvertently compromise privacy during reasoning by messaging humans, leaking context to peers, or executing unsafe tool calls. Existing approaches typically treat privacy as a binary constraint, overlooking nuanced, computation-dependent requirements. Furthermore, Large Language Model (LLM) agents are inherently probabilistic, lacking formal guarantees for security-critical operations. To address this, we introduce AgentCrypt, a three-tiered framework for secure agent communication that adds a deterministic protection layer atop any AI platform. AgentCrypt spans the full spectrum of privacy needs: from unrestricted data exchange (Level 1), to context-aware masking (Level 2), up to fully encrypted computation using Homomorphic Encryption (Level 3). Unlike prompt-based defenses, our approach guarantees that tagged data privacy is strictly preserved even when the underlying model errs. Security is decoupled from the agent's probabilistic reasoning, ensuring sensitive data remains protected throughout the computational lifecycle. AgentCrypt enables collaborative computation on otherwise inaccessible data, overcoming barriers like data silos. We implemented and validated it using LangGraph and Google ADK, demonstrating versatility across architectures. Finally, we introduce a benchmark dataset simulating privacy-critical tasks to enable systematic evaluation and foster the development of trustworthy, regulatable machine learning systems.

Leo Ardon, Daniel Furelos-Blanco, Alessandra Russo

This paper presents a novel approach to Multi-Agent Reinforcement Learning (MARL) that combines cooperative task decomposition with the learning of reward machines (RMs) encoding the structure of the sub-tasks. The proposed method helps deal with the non-Markovian nature of the rewards in partially observable environments and improves the interpretability of the learnt policies required to complete the cooperative task. The RMs associated with each sub-task are learnt in a decentralised manner and then used to guide the behaviour of each agent. By doing so, the complexity of a cooperative multi-agent problem is reduced, allowing for more effective learning. The results suggest that our approach is a promising direction for future research in MARL, especially in complex environments with large state spaces and multiple agents.

Nelson Vadori, Leo Ardon, Sumitra Ganesh et al.

We study a game between liquidity provider and liquidity taker agents interacting in an over-the-counter market, for which the typical example is foreign exchange. We show how a suitable design of parameterized families of reward functions coupled with shared policy learning constitutes an efficient solution to this problem. By playing against each other, our deep-reinforcement-learning-driven agents learn emergent behaviors relative to a wide spectrum of objectives encompassing profit-and-loss, optimal execution and market share. In particular, we find that liquidity providers naturally learn to balance hedging and skewing, where skewing refers to setting their buy and sell prices asymmetrically as a function of their inventory. We further introduce a novel RL-based calibration algorithm which we found performed well at imposing constraints on the game equilibrium. On the theoretical side, we are able to show convergence rates for our multi-agent policy gradient algorithm under a transitivity assumption, closely related to generalized ordinal potential games.

Leo Ardon, Alberto Pozanco, Daniel Borrajo et al.

Reinforcement Learning (RL) algorithms are known to scale poorly to environments with many available actions, requiring numerous samples to learn an optimal policy. The traditional approach of considering the same fixed action space in every possible state implies that the agent must understand, while also learning to maximize its reward, to ignore irrelevant actions such as $\textit{inapplicable actions}$ (i.e. actions that have no effect on the environment when performed in a given state). Knowing this information can help reduce the sample complexity of RL algorithms by masking the inapplicable actions from the policy distribution to only explore actions relevant to finding an optimal policy. While this technique has been formalized for quite some time within the Automated Planning community with the concept of precondition in the STRIPS language, RL algorithms have never formally taken advantage of this information to prune the search space to explore. This is typically done in an ad-hoc manner with hand-crafted domain logic added to the RL algorithm. In this paper, we propose a more systematic approach to introduce this knowledge into the algorithm. We (i) standardize the way knowledge can be manually specified to the agent; and (ii) present a new framework to autonomously learn the partial action model encapsulating the precondition of an action jointly with the policy. We show experimentally that learning inapplicable actions greatly improves the sample efficiency of the algorithm by providing a reliable signal to mask out irrelevant actions. Moreover, we demonstrate that thanks to the transferability of the knowledge acquired, it can be reused in other tasks and domains to make the learning process more efficient.

Roko Parac, Lorenzo Nodari, Leo Ardon et al.

This paper presents PROB-IRM, an approach that learns robust reward machines (RMs) for reinforcement learning (RL) agents from noisy execution traces. The key aspect of RM-driven RL is the exploitation of a finite-state machine that decomposes the agent's task into different subtasks. PROB-IRM uses a state-of-the-art inductive logic programming framework robust to noisy examples to learn RMs from noisy traces using the Bayesian posterior degree of beliefs, thus ensuring robustness against inconsistencies. Pivotal for the results is the interleaving between RM learning and policy learning: a new RM is learned whenever the RL agent generates a trace that is believed not to be accepted by the current RM. To speed up the training of the RL agent, PROB-IRM employs a probabilistic formulation of reward shaping that uses the posterior Bayesian beliefs derived from the traces. Our experimental analysis shows that PROB-IRM can learn (potentially imperfect) RMs from noisy traces and exploit them to train an RL agent to solve its tasks successfully. Despite the complexity of learning the RM from noisy traces, agents trained with PROB-IRM perform comparably to agents provided with handcrafted RMs.

Benjamin Patrick Evans, Sumitra Ganesh, Leo Ardon

Large language models (LLMs) achieve remarkable generative performance, yet their output quality is dependent on the decoding strategy. While sampling-based methods (e.g., top-k, nucleus) and search-and-select based methods (e.g., beam search, best-of-n, majority voting) can improve upon greedy decoding, both approaches suffer from limitations: sampling generally commits to a single path, while search often expends excessive computation regardless of task complexity. To address these, we introduce Entropy-informed decoding (EDEN), a plug-and-play, model-agnostic decoding framework that adaptively allocates computation based on the model's own uncertainty, approximating higher-width beam search with fewer expansions. At each generation step, EDEN estimates the entropy of the output token distribution and adjusts the branching factor monotonically with the entropy, expanding more candidates in high-entropy regions and following a greedier path in low-entropy regions, improving token efficiency. Experiments across complex tasks, including mathematical reasoning, code generation, and scientific questions, demonstrate that EDEN consistently improves output quality over existing decoding strategies, achieving better accuracy-expansion trade-offs than fixed-width beam search. By treating next-token selection as a noisy maximisation problem, we prove that branching factors monotone in entropy are guaranteed to find better (i.e. more probable) continuations than any fixed branching factor within the same total expansion budget, and derive explicit regret rates characterising the benefit of the adaptive allocation.

Benjamin Patrick Evans, Sihan Zeng, Sumitra Ganesh et al.

Agent-based models (ABMs) are valuable for modelling complex, potentially out-of-equilibria scenarios. However, ABMs have long suffered from the Lucas critique, stating that agent behaviour should adapt to environmental changes. Furthermore, the environment itself often adapts to these behavioural changes, creating a complex bi-level adaptation problem. Recent progress integrating multi-agent reinforcement learning into ABMs introduces adaptive agent behaviour, beginning to address the first part of this critique, however, the approaches are still relatively ad hoc, lacking a general formulation, and furthermore, do not tackle the second aspect of simultaneously adapting environmental level characteristics in addition to the agent behaviours. In this work, we develop a generic two-layer framework for ADaptive AGEnt based modelling (ADAGE) for addressing these problems. This framework formalises the bi-level problem as a Stackelberg game with conditional behavioural policies, providing a consolidated framework for adaptive agent-based modelling based on solving a coupled set of non-linear equations. We demonstrate how this generic approach encapsulates several common (previously viewed as distinct) ABM tasks, such as policy design, calibration, scenario generation, and robust behavioural learning under one unified framework. We provide example simulations on multiple complex economic and financial environments, showing the strength of the novel framework under these canonical settings, addressing long-standing critiques of traditional ABMs.

Leo Ardon, Daniel Furelos-Blanco, Roko Parac et al.

Reward machines (RMs) are an effective approach for addressing non-Markovian rewards in reinforcement learning (RL) through finite-state machines. Traditional RMs, which label edges with propositional logic formulae, inherit the limited expressivity of propositional logic. This limitation hinders the learnability and transferability of RMs since complex tasks will require numerous states and edges. To overcome these challenges, we propose First-Order Reward Machines ($\texttt{FORM}$s), which use first-order logic to label edges, resulting in more compact and transferable RMs. We introduce a novel method for $\textbf{learning}$ $\texttt{FORM}$s and a multi-agent formulation for $\textbf{exploiting}$ them and facilitate their transferability, where multiple agents collaboratively learn policies for a shared $\texttt{FORM}$. Our experimental results demonstrate the scalability of $\texttt{FORM}$s with respect to traditional RMs. Specifically, we show that $\texttt{FORM}$s can be effectively learnt for tasks where traditional RM learning approaches fail. We also show significant improvements in learning speed and task transferability thanks to the multi-agent learning framework and the abstraction provided by the first-order language.

Giuseppe Canonaco, Leo Ardon, Alberto Pozanco et al.

The use of Potential-Based Reward Shaping (PBRS) has shown great promise in the ongoing research effort to tackle sample inefficiency in Reinforcement Learning (RL). However, choosing the right potential function remains an open challenge. Additionally, RL techniques are usually constrained to use a finite horizon for computational limitations, which introduces a bias when using PBRS. In this paper, we first build some theoretically-grounded intuition on why selecting the potential function as the optimal value function of the task at hand produces performance advantages. We then analyse the bias induced by finite horizons in the context of PBRS producing novel insights. Finally, leveraging abstractions as a way to approximate the optimal value function of the given task, we assess the sample efficiency and performance impact of PBRS on four environments including a goal-oriented navigation task and three Arcade Learning Environments (ALE) games. Remarkably, experimental results show that we can reach the same level of performance as CNN-based solutions with a simple fully-connected network.

Deepeka Garg, Sihan Zeng, Sumitra Ganesh et al.

In this paper, we address the challenges of managing Standard Operating Procedures (SOPs), which often suffer from inconsistencies in language, format, and execution, leading to operational inefficiencies. Traditional process modeling demands significant manual effort, domain expertise, and familiarity with complex languages like Business Process Modeling Notation (BPMN), creating barriers for non-techincal users. We introduce SOP Structuring (SOPStruct), a novel approach that leverages Large Language Models (LLMs) to transform SOPs into decision-tree-based structured representations. SOPStruct produces a standardized representation of SOPs across different domains, reduces cognitive load, and improves user comprehension by effectively capturing task dependencies and ensuring sequential integrity. Our approach enables leveraging the structured information to automate workflows as well as empower the human users. By organizing procedures into logical graphs, SOPStruct facilitates backtracking and error correction, offering a scalable solution for process optimization. We employ a novel evaluation framework, combining deterministic methods with the Planning Domain Definition Language (PDDL) to verify graph soundness, and non-deterministic assessment by an LLM to ensure completeness. We empirically validate the robustness of our LLM-based structured SOP representation methodology across SOPs from different domains and varying levels of complexity. Despite the current lack of automation readiness in many organizations, our research highlights the transformative potential of LLMs to streamline process modeling, paving the way for future advancements in automated procedure optimization.

Deepeka Garg, Sihan Zeng, Annapoorani L. Narayanan et al.

Learning to autonomously execute long-horizon procedures from natural language remains a core challenge for intelligent agents. Free-form instructions such as recipes, scientific protocols, or business workflows encode rich procedural knowledge, but their variability and lack of structure cause agents driven by large language models (LLMs) to drift or fail during execution. We introduce Procedure Aware DynaMic Execution (PADME), an agent framework that produces and exploits a graph-based representation of procedures. Unlike prior work that relies on manual graph construction or unstructured reasoning, PADME autonomously transforms procedural text into executable graphs that capture task dependencies, decision points, and reusable subroutines. Central to PADME is a two-phase methodology; Teach phase, which focuses on systematic structuring, enrichment with executable logic of procedures, followed by Execute phase, which enables dynamic execution in response to real-time inputs and environment feedback. This separation ensures quality assurance and scalability, allowing expert knowledge to be encoded once and reliably reused across varying contexts. The graph representation also provides an inductive bias that reduces error accumulation in long-horizon reasoning, underscoring the importance of structured procedure modeling for reliable agent-driven automation. Empirically, PADME achieves state-of-the-art performance on four diverse benchmarks, including ALFWorld and ScienceWorld. These results demonstrate that agents equipped with graph-based procedure representations offer a powerful intermediate abstraction for robust and generalizable execution.

Sihan Zeng, Benjamin Patrick Evans, Sujay Bhatt et al.

We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

Benjamin Patrick Evans, Leo Ardon, Sumitra Ganesh

Modelling bounded rational decision-making through information constrained processing provides a principled approach for representing departures from rationality within a reinforcement learning framework, while still treating decision-making as an optimization process. However, existing approaches are generally based on Entropy, Kullback-Leibler divergence, or Mutual Information. In this work, we highlight issues with these approaches when dealing with ordinal action spaces. Specifically, entropy assumes uniform prior beliefs, missing the impact of a priori biases on decision-makings. KL-Divergence addresses this, however, has no notion of "nearness" of actions, and additionally, has several well known potentially undesirable properties such as the lack of symmetry, and furthermore, requires the distributions to have the same support (e.g. positive probability for all actions). Mutual information is often difficult to estimate. Here, we propose an alternative approach for modeling bounded rational RL agents utilising Wasserstein distances. This approach overcomes the aforementioned issues. Crucially, this approach accounts for the nearness of ordinal actions, modeling "stickiness" in agent decisions and unlikeliness of rapidly switching to far away actions, while also supporting low probability actions, zero-support prior distributions, and is simple to calculate directly.

Leo Ardon, Benjamin Patrick Evans, Deepeka Garg et al.

We develop a novel two-layer approach for optimising mortgage relief products through a simulated multi-agent mortgage environment. While the approach is generic, here the environment is calibrated to the US mortgage market based on publicly available census data and regulatory guidelines. Through the simulation layer, we assess the resilience of households to exogenous income shocks, while the optimisation layer explores strategies to improve the robustness of households to these shocks by making novel mortgage assistance products available to households. Households in the simulation are adaptive, learning to make mortgage-related decisions (such as product enrolment or strategic foreclosures) that maximize their utility, balancing their available liquidity and equity. We show how this novel two-layer simulation approach can successfully design novel mortgage assistance products to improve household resilience to exogenous shocks, and balance the costs of providing such products through post-hoc analysis. Previously, such analysis could only be conducted through expensive pilot studies involving real participants, demonstrating the benefit of the approach for designing and evaluating financial products.

Leo Ardon

In this paper, we evaluate the use of Reinforcement Learning (RL) to solve a classic combinatorial optimization problem: the Capacitated Vehicle Routing Problem (CVRP). We formalize this problem in the RL framework and compare two of the most promising RL approaches with traditional solving techniques on a set of benchmark instances. We measure the different approaches with the quality of the solution returned and the time required to return it. We found that despite not returning the best solution, the RL approach has many advantages over traditional solvers. First, the versatility of the framework allows the resolution of more complex combinatorial problems. Moreover, instead of trying to solve a specific instance of the problem, the RL algorithm learns the skills required to solve the problem. The trained policy can then quasi instantly provide a solution to an unseen problem without having to solve it from scratch. Finally, the use of trained models makes the RL solver by far the fastest, and therefore make this approach more suited for commercial use where the user experience is paramount. Techniques like Knowledge Transfer can also be used to improve the training efficiency of the algorithm and help solve bigger and more complex problems.

Leo Ardon, Nelson Vadori, Thomas Spooner et al.

We present a new financial framework where two families of RL-based agents representing the Liquidity Providers and Liquidity Takers learn simultaneously to satisfy their objective. Thanks to a parametrized reward formulation and the use of Deep RL, each group learns a shared policy able to generalize and interpolate over a wide range of behaviors. This is a step towards a fully RL-based market simulator replicating complex market conditions particularly suited to study the dynamics of the financial market under various scenarios.