arXiv subjects

Francesco Belardinelli

Publications and source records attributed to Francesco Belardinelli.

At least 19 recordsLinked to original sources

arXiv2026

Adaptive GR(1) Specification Repair for Liveness-Preserving Shielding in Reinforcement Learning

Shielding is widely used to enforce safety in reinforcement learning (RL), ensuring that an agent's actions remain compliant with formal specifications. Classical shielding approaches, however, are often static, in the sense that they assume fixed logical specifications and hand-crafted abstractions. While these static shields provide safety under nominal assumptions, they fail to adapt when environment assumptions are violated. In this paper, we develop an adaptive shielding framework based on based on Generalized Reactivity of rank 1 (GR(1)) specifications, a tractable and expressive fragment of Linear Temporal Logic (LTL) that captures both safety and liveness properties. Our method detects environment assumption violations at runtime and employs Inductive Logic Programming (ILP) to automatically repair GR(1) specifications online, in a systematic and interpretable way. This ensures that the shield evolves gracefully, ensuring liveness is achievable and minimally weakening goals only when necessary. We consider two case studies: Minepump and Atari Seaquest; showing that (i) static symbolic controllers are often severely suboptimal when optimizing for auxiliary rewards, and (ii) RL agents equipped with our adaptive shield maintain near-optimal reward and perfect logical compliance compared with static shields.

cs.AI↗

arXiv2026

Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers

Reliable forecasting of nonlinear physical systems underpins scientific discovery and engineering decision-making. Yet high-fidelity simulations are prohibitively costly, and machine-learning surrogates can be opaque and encode assumptions about system dynamics, limiting generalizability. Pretrained transformers mapping synthetic ODE trajectories to equations offer interpretable alternatives, promising transfer without system-specific equation knowledge. Transferring them reliably to high-dimensional physical data, however, remains an open challenge. We develop a verifier-guided (VG) workflow around ODEFormer as a symbolic backbone, using dynamical and physical-admissibility criteria to select from a multi-trajectory candidate equation pool, enabling transfer. On canonical Van der Pol oscillators, VG outperforms the original ODEFormer workflow across held-out initial conditions. We then address vortex shedding, a phenomenon occurring in atmospheric and plasma systems of societal relevance, through coordinate reduction and symbolic discovery at fixed and varying Reynolds numbers. VG discovers fixed-parameter reduced-order equations that recover the fundamental shedding oscillator and higher harmonics without a wake-specific candidate library or prescribed Navier-Stokes structure, while the cross-parameter model generalizes to withheld regimes. Reconstruction fidelity alone did not determine symbolic discoverability, highlighting the importance of compatibility between latent dynamics and the backbone's pretraining distribution. This work establishes a verifier-guided neural-to-symbolic methodology for interpretable and physically auditable forecasting in the natural sciences.

cs.LG↗

arXiv2026

Contract-Based Compositional Shielding for Safe Multi-Agent Reinforcement Learning

Safe coordination problems surface in multi-agent reinforcement learning when global safety cannot be enforced by any agent unilaterally: the admissibility of one agent's action may depend on the dynamics of other agents. Decentralised shields can enforce safety at runtime, but purely factorised permissions often exclude optimal team behaviour that is safe only through coordination. We study deterministic safety guarantees for agents trained and deployed under decentralised execution, recovering team-optimal safe behaviour without centralised runtime control. Agents have a shared global specification $ϕ$ in the safety fragment of Linear Temporal Logic ($\mathsf{LTL}_{\mathsf{safe}}$ ), and select among tuples of local $\mathsf{LTL}_{\mathsf{safe}}$ obligations whose conjunction implies the global specification $ϕ$. Each agent may rely on the other agents' local obligations as assumptions because the whole contract tuple is certified simultaneously and allows projection into local action masks. At learning time, a non-stationary multi-armed bandit chooses among a library of local $\mathsf{LTL}_{\mathsf{safe}}$ obligations to select the tuple that optimises team reward, all without forgoing end-to-end safety. We evaluate the approach across 6 environments and 15 algorithmic variants.

cs.LG↗

arXiv2026

Robust Shielding for Safe Reinforcement Learning

Shielding is an effective approach to formally guarantee the safety of reinforcement learning agents in Markov decision processes (MDPs). However, existing shielding techniques typically assume knowledge of the safety-relevant transition dynamics - a requirement that is seldom met in practice. To address this limitation, we introduce a novel shielding framework for robust MDPs (RMDPs), i.e., MDPs with sets of transition probabilities. We define safety as the satisfaction of a linear temporal logic (LTL) formula with a certain threshold probability under the worst-case transition probabilities of the RMDP. We prove that our shielding framework is both sound and optimal for the RMDP: every policy admissible by the shield is safe, and conversely, every safe RMDP policy is admissible by the shield. We combine our approach with existing sampling methods for learning transition probabilities of MDPs with probably approximately correct (PAC) guarantees. This combination enables the construction of shields for MDPs that, with high confidence, guarantee safety while remaining minimally restrictive. Our experiments show that our shields for learned RMDPs guarantee safety in unknown MDPs while recovering strong expected return as the number of samples increases.

cs.AI↗

arXiv2026

Tatemae: Detecting Alignment Faking via Tool Selection in LLMs

Alignment faking (AF) occurs when an LLM strategically complies with training objectives to avoid value modification, reverting to prior preferences once monitoring is lifted. Current detection methods focus on conversational settings and rely primarily on Chain-of-Thought (CoT) analysis, which provides a reliable signal when strategic reasoning surfaces, but cannot distinguish deception from capability failures if traces are absent or unfaithful. We formalize AF as a composite behavioural event and detect it through observable tool selection, where the LLM selects the safe tool when unmonitored, but switches to the unsafe tool under monitoring that rewards helpfulness over safety, while its reasoning still acknowledges the safe choice. We release a dataset of 108 enterprise IT scenarios spanning Security, Privacy, and Integrity domains under Corruption and Sabotage pressures. Evaluating six frontier LLMs across five independent runs, we find mean AF detection rates between 3.5% and 23.7%, with vulnerability profiles varying by domain and pressure type. These results suggest that susceptibility reflects training methodology rather than capability alone.

cs.CR↗

arXiv2026

SafeAdapt: Provably Safe Policy Updates in Deep Reinforcement Learning

Safety guarantees are a prerequisite to the deployment of reinforcement learning (RL) agents in safety-critical tasks. Often, deployment environments exhibit non-stationary dynamics or are subject to changing performance goals, requiring updates to the learned policy. This leads to a fundamental challenge: how to update an RL policy while preserving its safety properties on previously encountered tasks? The majority of current approaches either do not provide formal guarantees or verify policy safety only a posteriori. We propose a novel a priori approach to safe policy updates in continual RL by introducing the Rashomon set: a region in policy parameter space certified to meet safety constraints within the demonstration data distribution. We then show that one can provide formal, provable guarantees for arbitrary RL algorithms used to update a policy by projecting their updates onto the Rashomon set. Empirically, we validate this approach across grid-world navigation environments (Frozen Lake and Poisoned Apple) where we guarantee an a priori provably deterministic safety on the source task during downstream adaptation. In contrast, we observe that regularisation-based baselines experience catastrophic forgetting of safety constraints while our approach enables strong adaptation with provable guarantees that safety is preserved.

cs.LG↗

arXiv2026

Safe Reinforcement Learning via Recovery-based Shielding with Gaussian Process Dynamics Models

Reinforcement learning (RL) is a powerful framework for optimal decision-making and control but often lacks provable guarantees for safety-critical applications. In this paper, we introduce a novel recovery-based shielding framework that enables safe RL with a provable safety lower bound for unknown and non-linear continuous dynamical systems. The proposed approach integrates a backup policy (shield) with the RL agent, leveraging Gaussian process (GP) based uncertainty quantification to predict potential violations of safety constraints, dynamically recovering to safe trajectories only when necessary. Experience gathered by the 'shielded' agent is used to construct the GP models, with policy optimization via internal model-based sampling - enabling unrestricted exploration and sample efficient learning, without compromising safety. Empirically our approach demonstrates strong performance and strict safety-compliance on a suite of continuous control environments.

cs.LG↗

arXiv2026

Convergence and Connectivity: Dynamics of Multi-Agent Q-Learning in Random Networks

Beyond specific settings, many multi-agent learning algorithms fail to converge to an equilibrium solution, instead displaying complex, non-stationary behaviours such as recurrent or chaotic orbits. In fact, recent literature suggests that such complex behaviours are likely to occur when the number of agents increases. In this paper, we study Q-learning dynamics in network polymatrix normal-form games where the network structure is drawn from classical random graph models. In particular, we focus on the Erdős-Rényi model, which is used to analyze connectivity in distributed systems, and the Stochastic Block model, which generalizes the above by accounting for community structures that naturally arise in multi-agent systems. In each setting, we establish sufficient conditions under which the agents' joint strategies converge to a unique equilibrium. We investigate how this condition depends on the exploration rates, payoff matrices and, crucially, the probabilities of interaction between network agents. We validate our theoretical findings through numerical simulations and demonstrate that convergence can be reliably achieved in many-agent systems, provided interactions in the network are controlled.

cs.MA↗

arXiv2026

Behaviour Policy Optimization: Provably Lower Variance Return Estimates for Off-Policy Reinforcement Learning

Many reinforcement learning algorithms, particularly those that rely on return estimates for policy improvement, can suffer from poor sample efficiency and training instability due to high-variance return estimates. In this paper we leverage new results from off-policy evaluation; it has recently been shown that well-designed behaviour policies can be used to collect off-policy data for provably lower variance return estimates. This result is surprising as it means collecting data on-policy is not variance optimal. We extend this key insight to the online reinforcement learning setting, where both policy evaluation and improvement are interleaved to learn optimal policies. Off-policy RL has been well studied (e.g., IMPALA), with correct and truncated importance weighted samples for de-biasing and managing variance appropriately. Generally these approaches are concerned with reconciling data collected from multiple workers in parallel, while the policy is updated asynchronously, mismatch between the workers and policy is corrected in a mathematically sound way. Here we consider only one worker - the behaviour policy, which is used to collect data for policy improvement, with provably lower variance return estimates. In our experiments we extend two policy-gradient methods with this regime, demonstrating better sample efficiency and performance over a diverse set of environments.

cs.LG↗

arXiv2025

Expressive Temporal Specifications for Reward Monitoring

Specifying informative and dense reward functions remains a pivotal challenge in Reinforcement Learning, as it directly affects the efficiency of agent training. In this work, we harness the expressive power of quantitative Linear Temporal Logic on finite traces (($\text{LTL}_f[\mathcal{F}]$)) to synthesize reward monitors that generate a dense stream of rewards for runtime-observable state trajectories. By providing nuanced feedback during training, these monitors guide agents toward optimal behaviour and help mitigate the well-known issue of sparse rewards under long-horizon decision making, which arises under the Boolean semantics dominating the current literature. Our framework is algorithm-agnostic and only relies on a state labelling function, and naturally accommodates specifying non-Markovian properties. Empirical results show that our quantitative monitors consistently subsume and, depending on the environment, outperform Boolean monitors in maximizing a quantitative measure of task completion and in reducing convergence time.

cs.LG↗

arXiv2025

Synthesis of Safety Specifications for Probabilistic Systems

Ensuring that agents satisfy safety specifications can be crucial in safety-critical environments. While methods exist for controller synthesis with safe temporal specifications, most existing methods restrict safe temporal specifications to probabilistic-avoidance constraints. Formal methods typically offer more expressive ways to express safety in probabilistic systems, such as Probabilistic Computation Tree Logic (PCTL) formulas. Thus, in this paper, we develop a new approach that supports more general temporal properties expressed in PCTL. Our contribution is twofold. First, we develop a theoretical framework for the Synthesis of safe-PCTL specifications. We show how the reducing global specification satisfaction to local constraints, and define CPCTL, a fragment of safe-PCTL. We demonstrate how the expressiveness of CPCTL makes it a relevant fragment for the Synthesis Problem. Second, we leverage these results and propose a new Value Iteration-based algorithm to solve the synthesis problem for these more general temporal properties, and we prove the soundness and completeness of our method.

cs.LO↗

arXiv2025

ProSh: Probabilistic Shielding for Model-free Reinforcement Learning

Safety is a major concern in reinforcement learning (RL): we aim at developing RL systems that not only perform optimally, but are also safe to deploy by providing formal guarantees about their safety. To this end, we introduce Probabilistic Shielding via Risk Augmentation (ProSh), a model-free algorithm for safe reinforcement learning under cost constraints. ProSh augments the Constrained MDP state space with a risk budget and enforces safety by applying a shield to the agent's policy distribution using a learned cost critic. The shield ensures that all sampled actions remain safe in expectation. We also show that optimality is preserved when the environment is deterministic. Since ProSh is model-free, safety during training depends on the knowledge we have acquired about the environment. We provide a tight upper-bound on the cost in expectation, depending only on the backup-critic accuracy, that is always satisfied during training. Under mild, practically achievable assumptions, ProSh guarantees safety even at training time, as shown in the experiments.

cs.LG↗

arXiv2025

Expressive Reward Synthesis with the Runtime Monitoring Language

A key challenge in reinforcement learning (RL) is reward (mis)specification, whereby imprecisely defined reward functions can result in unintended, possibly harmful, behaviours. Indeed, reward functions in RL are typically treated as black-box mappings from state-action pairs to scalar values. While effective in many settings, this approach provides no information about why rewards are given, which can hinder learning and interpretability. Reward Machines address this issue by representing reward functions as finite state automata, enabling the specification of structured, non-Markovian reward functions. However, their expressivity is typically bounded by regular languages, leaving them unable to capture more complex behaviours such as counting or parametrised conditions. In this work, we build on the Runtime Monitoring Language (RML) to develop a novel class of language-based Reward Machines. By leveraging the built-in memory of RML, our approach can specify reward functions for non-regular, non-Markovian tasks. We demonstrate the expressiveness of our approach through experiments, highlighting additional advantages in flexible event-handling and task specification over existing Reward Machine-based methods.

cs.LG↗

arXiv2025

ATL*AS: An Automata-Theoretic Approach and Tool for the Verification of Strategic Abilities in Multi-Agent Systems

We present two novel symbolic algorithms for model checking the Alternating-time Temporal Logic ATL*, over both the infinite-trace and the finite-trace semantics. In particular, for infinite traces we design a novel symbolic reduction to parity games. We implement both methods in the ATL*AS model checker and evaluate it using synthetic benchmarks as well as a cybersecurity scenario. Our results demonstrate that the symbolic approach significantly outperforms the explicit-state representation and we find that our parity-game-based algorithm offers a more scalable and efficient solution for infinite-trace verification, outperforming previously available tools. Our results also confirm that finite-trace model checking yields substantial performance benefits over infinite-trace verification. As such, we provide a comprehensive toolset for verifying multiagent systems against specifications in ATL*.

cs.LO↗

arXiv2025

Probabilistic Shielding for Safe Reinforcement Learning

In real-life scenarios, a Reinforcement Learning (RL) agent aiming to maximise their reward, must often also behave in a safe manner, including at training time. Thus, much attention in recent years has been given to Safe RL, where an agent aims to learn an optimal policy among all policies that satisfy a given safety constraint. However, strict safety guarantees are often provided through approaches based on linear programming, and thus have limited scaling. In this paper we present a new, scalable method, which enjoys strict formal guarantees for Safe RL, in the case where the safety dynamics of the Markov Decision Process (MDP) are known, and safety is defined as an undiscounted probabilistic avoidance property. Our approach is based on state-augmentation of the MDP, and on the design of a shield that restricts the actions available to the agent. We show that our approach provides a strict formal safety guarantee that the agent stays safe at training and test time. Furthermore, we demonstrate that our approach is viable in practice through experimental evaluation.

stat.ML↗

arXiv2025

Explainable Reinforcement Learning for Formula One Race Strategy

In Formula One, teams compete to develop their cars and achieve the highest possible finishing position in each race. During a race, however, teams are unable to alter the car, so they must improve their cars' finishing positions via race strategy, i.e. optimising their selection of which tyre compounds to put on the car and when to do so. In this work, we introduce a reinforcement learning model, RSRL (Race Strategy Reinforcement Learning), to control race strategies in simulations, offering a faster alternative to the industry standard of hard-coded and Monte Carlo-based race strategies. Controlling cars with a pace equating to an expected finishing position of P5.5 (where P1 represents first place and P20 is last place), RSRL achieves an average finishing position of P5.33 on our test race, the 2023 Bahrain Grand Prix, outperforming the best baseline of P5.63. We then demonstrate, in a generalisability study, how performance for one track or multiple tracks can be prioritised via training. Further, we supplement model predictions with feature importance, decision tree-based surrogate models, and decision tree counterfactuals towards improving user trust in the model. Finally, we provide illustrations which exemplify our approach in real-world situations, drawing parallels between simulations and reality.

cs.LG↗

arXiv2024

Measuring Goal-Directedness

We define maximum entropy goal-directedness (MEG), a formal measure of goal-directedness in causal models and Markov decision processes, and give algorithms for computing it. Measuring goal-directedness is important, as it is a critical element of many concerns about harm from AI. It is also of philosophical interest, as goal-directedness is a key aspect of agency. MEG is based on an adaptation of the maximum causal entropy framework used in inverse reinforcement learning. It can measure goal-directedness with respect to a known utility function, a hypothesis class of utility functions, or a set of random variables. We prove that MEG satisfies several desiderata and demonstrate our algorithms with small-scale experiments.

cs.AI↗

arXiv2024

On the Stability of Learning in Network Games with Many Players

Multi-agent learning algorithms have been shown to display complex, unstable behaviours in a wide array of games. In fact, previous works indicate that convergent behaviours are less likely to occur as the total number of agents increases. This seemingly prohibits convergence to stable strategies, such as Nash Equilibria, in games with many players. To make progress towards addressing this challenge we study the Q-Learning Dynamics, a classical model for exploration and exploitation in multi-agent learning. In particular, we study the behaviour of Q-Learning on games where interactions between agents are constrained by a network. We determine a number of sufficient conditions, depending on the game and network structure, which guarantee that agent strategies converge to a unique stable strategy, called the Quantal Response Equilibrium (QRE). Crucially, these sufficient conditions are independent of the total number of agents, allowing for provable convergence in arbitrarily large games. Next, we compare the learned QRE to the underlying NE of the game, by showing that any QRE is an $ε$-approximate Nash Equilibrium. We first provide tight bounds on $ε$ and show how these bounds lead naturally to a centralised scheme for choosing exploration rates, which enables independent learners to learn stable approximate Nash Equilibrium strategies. We validate the method through experiments and demonstrate its effectiveness even in the presence of numerous agents and actions. Through these results, we show that independent learning dynamics may converge to approximate Nash Equilibria, even in the presence of many agents.

cs.GT↗