arXiv subjects

Francesco Belardinelli

Publications and source records attributed to Francesco Belardinelli.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2024

The Reasons that Agents Act: Intention and Instrumental Goals

Intention is an important and challenging concept in AI. It is important because it underlies many other concepts we care about, such as agency, manipulation, legal responsibility, and blame. However, ascribing intent to AI systems is contentious, and there is no universally accepted theory of intention applicable to AI agents. We operationalise the intention with which an agent acts, relating to the reasons it chooses its decision. We introduce a formal definition of intention in structural causal influence models, grounded in the philosophy literature on intent and applicable to real-world machine learning systems. Through a number of examples and results, we show that our definition captures the intuitive notion of intent and satisfies desiderata set-out by past work. In addition, we show how our definition relates to past concepts, including actual causality, and the notion of instrumental goals, which is a core idea in the literature on safe AI agents. Finally, we demonstrate how our definition can be used to infer the intentions of reinforcement learning agents and language models from their behaviour.

cs.AI↗

arXiv2024

Leveraging Approximate Model-based Shielding for Probabilistic Safety Guarantees in Continuous Environments

Shielding is a popular technique for achieving safe reinforcement learning (RL). However, classical shielding approaches come with quite restrictive assumptions making them difficult to deploy in complex environments, particularly those with continuous state or action spaces. In this paper we extend the more versatile approximate model-based shielding (AMBS) framework to the continuous setting. In particular we use Safety Gym as our test-bed, allowing for a more direct comparison of AMBS with popular constrained RL algorithms. We also provide strong probabilistic safety guarantees for the continuous setting. In addition, we propose two novel penalty techniques that directly modify the policy gradient, which empirically provide more stable convergence in our experiments.

cs.LG↗

arXiv2023

Stability of Multi-Agent Learning in Competitive Networks: Delaying the Onset of Chaos

The behaviour of multi-agent learning in competitive network games is often studied within the context of zero-sum games, in which convergence guarantees may be obtained. However, outside of this class the behaviour of learning is known to display complex behaviours and convergence cannot be always guaranteed. Nonetheless, in order to develop a complete picture of the behaviour of multi-agent learning in competitive settings, the zero-sum assumption must be lifted. Motivated by this we study the Q-Learning dynamics, a popular model of exploration and exploitation in multi-agent learning, in competitive network games. We determine how the degree of competition, exploration rate and network connectivity impact the convergence of Q-Learning. To study generic competitive games, we parameterise network games in terms of correlations between agent payoffs and study the average behaviour of the Q-Learning dynamics across all games drawn from a choice of this parameter. This statistical approach establishes choices of parameters for which Q-Learning dynamics converge to a stable fixed point. Differently to previous works, we find that the stability of Q-Learning is explicitly dependent only on the network connectivity rather than the total number of agents. Our experiments validate these findings and show that, under certain network structures, the total number of agents can be increased without increasing the likelihood of unstable or chaotic behaviours.

cs.GT↗

arXiv2023

Honesty Is the Best Policy: Defining and Mitigating AI Deception

Deceptive agents are a challenge for the safety, trustworthiness, and cooperation of AI systems. We focus on the problem that agents might deceive in order to achieve their goals (for instance, in our experiments with language models, the goal of being evaluated as truthful). There are a number of existing definitions of deception in the literature on game theory and symbolic AI, but there is no overarching theory of deception for learning agents in games. We introduce a formal definition of deception in structural causal games, grounded in the philosophy literature, and applicable to real-world machine learning systems. Several examples and results illustrate that our formal definition aligns with the philosophical and commonsense meaning of deception. Our main technical result is to provide graphical criteria for deception. We show, experimentally, that these results can be used to mitigate deception in reinforcement learning agents and language models.

cs.AI↗

arXiv2023

3vLTL: A Tool to Generate Automata for Three-valued LTL

Multi-valued logics have a long tradition in the literature on system verification, including run-time verification. However, comparatively fewer model-checking tools have been developed for multi-valued specification languages. We present 3vLTL, a tool to generate Buchi automata from formulas in Linear-time Temporal Logic (LTL) interpreted on a three-valued semantics. Given an LTL formula, a set of atomic propositions as the alphabet for the automaton, and a truth value, our procedure generates a Buchi automaton that accepts all the words that assign the chosen truth value to the LTL formula. Given the particular type of the output of the tool, it can also be seamlessly processed by third-party libraries in a natural way. That is, the Buchi automaton can then be used in the context of formal verification to check whether an LTL formula is true, false, or undefined on a given model.

cs.FL↗

arXiv2023

Scalable Verification of Strategy Logic through Three-valued Abstraction

The model checking problem for multi-agent systems against Strategy Logic specifications is known to be non-elementary. On this logic several fragments have been defined to tackle this issue but at the expense of expressiveness. In this paper, we propose a three-valued semantics for Strategy Logic upon which we define an abstraction method. We show that the latter semantics is an approximation of the classic two-valued one for Strategy Logic. Furthermore, we extend MCMAS, an open-source model checker for multi-agent specifications, to incorporate our abstraction method and present some promising experimental results.

cs.MA↗

arXiv2023

Strategic Abilities of Forgetful Agents in Stochastic Environments

In this paper, we investigate the probabilistic variants of the strategy logics ATL and ATL* under imperfect information. Specifically, we present novel decidability and complexity results when the model transitions are stochastic and agents play uniform strategies. That is, the semantics of the logics are based on multi-agent, stochastic transition systems with imperfect information, which combine two sources of uncertainty, namely, the partial observability agents have on the environment, and the likelihood of transitions to occur from a system state. Since the model checking problem is undecidable in general in this setting, we restrict our attention to agents with memoryless (positional) strategies. The resulting setting captures the situation in which agents have qualitative uncertainty of the local state and quantitative uncertainty about the occurrence of future events. We illustrate the usefulness of this setting with meaningful examples.

cs.MA↗

arXiv2023

Bisimulations for Verifying Strategic Abilities with an Application to the ThreeBallot Voting Protocol

We propose a notion of alternating bisimulation for strategic abilities under imperfect information. The bisimulation preserves formulas of ATL$^*$ for both the {\em objective} and {\em subjective} variants of the state-based semantics with imperfect information, which are commonly used in the modeling and verification of multi-agent systems. Furthermore, we apply the theoretical result to the verification of coercion-resistance in the ThreeBallot voting system, a voting protocol that does not use cryptography. In particular, we show that natural simplifications of an initial model of the protocol are in fact bisimulations of the original model, and therefore satisfy the same ATL$^*$ properties, including coercion-resistance. These simplifications allow the model-checking tool MCMAS to terminate on models with a larger number of voters and candidates, compared with the initial model.

cs.MA↗

arXiv2023

Approximate Model-Based Shielding for Safe Reinforcement Learning

Reinforcement learning (RL) has shown great potential for solving complex tasks in a variety of domains. However, applying RL to safety-critical systems in the real-world is not easy as many algorithms are sample-inefficient and maximising the standard RL objective comes with no guarantees on worst-case performance. In this paper we propose approximate model-based shielding (AMBS), a principled look-ahead shielding algorithm for verifying the performance of learned RL policies w.r.t. a set of given safety constraints. Our algorithm differs from other shielding approaches in that it does not require prior knowledge of the safety-relevant dynamics of the system. We provide a strong theoretical justification for AMBS and demonstrate superior performance to other safety-aware approaches on a set of Atari games with state-dependent safety-labels.

cs.LG↗

arXiv2023

Stability of Multi-Agent Learning: Convergence in Network Games with Many Players

The behaviour of multi-agent learning in many player games has been shown to display complex dynamics outside of restrictive examples such as network zero-sum games. In addition, it has been shown that convergent behaviour is less likely to occur as the number of players increase. To make progress in resolving this problem, we study Q-Learning dynamics and determine a sufficient condition for the dynamics to converge to a unique equilibrium in any network game. We find that this condition depends on the nature of pairwise interactions and on the network structure, but is explicitly independent of the total number of agents in the game. We evaluate this result on a number of representative network games and show that, under suitable network conditions, stable learning dynamics can be achieved with an arbitrary number of agents.

cs.GT↗

arXiv2023

Beyond Strict Competition: Approximate Convergence of Multi Agent Q-Learning Dynamics

The behaviour of multi-agent learning in competitive settings is often considered under the restrictive assumption of a zero-sum game. Only under this strict requirement is the behaviour of learning well understood; beyond this, learning dynamics can often display non-convergent behaviours which prevent fixed-point analysis. Nonetheless, many relevant competitive games do not satisfy the zero-sum assumption. Motivated by this, we study a smooth variant of Q-Learning, a popular reinforcement learning dynamics which balances the agents' tendency to maximise their payoffs with their propensity to explore the state space. We examine this dynamic in games which are `close' to network zero-sum games and find that Q-Learning converges to a neighbourhood around a unique equilibrium. The size of the neighbourhood is determined by the `distance' to the zero-sum game, as well as the exploration rates of the agents. We complement these results by providing a method whereby, given an arbitrary network game, the `nearest' network zero-sum game can be found efficiently. As our experiments show, these guarantees are independent of whether the dynamics ultimately reach an equilibrium, or remain non-convergent.

cs.GT↗

arXiv2023

Characterising Decision Theories with Mechanised Causal Graphs

How should my own decisions affect my beliefs about the outcomes I expect to achieve? If taking a certain action makes me view myself as a certain type of person, it might affect how I think others view me, and how I view others who are similar to me. This can influence my expected utility calculations and change which action I perceive to be best. Whether and how it should is subject to debate, with contenders for how to think about it including evidential decision theory, causal decision theory, and functional decision theory. In this paper, we show that mechanised causal models can be used to characterise and differentiate the most important decision theories, and generate a taxonomy of different decision theories.

cs.AI↗

arXiv2023

Approximate Shielding of Atari Agents for Safe Exploration

Balancing exploration and conservatism in the constrained setting is an important problem if we are to use reinforcement learning for meaningful tasks in the real world. In this paper, we propose a principled algorithm for safe exploration based on the concept of shielding. Previous approaches to shielding assume access to a safety-relevant abstraction of the environment or a high-fidelity simulator. Instead, our work is based on latent shielding - another approach that leverages world models to verify policy roll-outs in the latent space of a learned dynamics model. Our novel algorithm builds on this previous work, using safety critics and other additional features to improve the stability and farsightedness of the algorithm. We demonstrate the effectiveness of our approach by running experiments on a small set of Atari games with state dependent safety labels. We present preliminary results that show our approximate shielding algorithm effectively reduces the rate of safety violations, and in some cases improves the speed of convergence and quality of the final agent.

cs.AI↗

arXiv2023

Asymptotic Convergence and Performance of Multi-Agent Q-Learning Dynamics

Achieving convergence of multiple learning agents in general $N$-player games is imperative for the development of safe and reliable machine learning (ML) algorithms and their application to autonomous systems. Yet it is known that, outside the bounds of simple two-player games, convergence cannot be taken for granted. To make progress in resolving this problem, we study the dynamics of smooth Q-Learning, a popular reinforcement learning algorithm which quantifies the tendency for learning agents to explore their state space or exploit their payoffs. We show a sufficient condition on the rate of exploration such that the Q-Learning dynamics is guaranteed to converge to a unique equilibrium in any game. We connect this result to games for which Q-Learning is known to converge with arbitrary exploration rates, including weighted Potential games and weighted zero sum polymatrix games. Finally, we examine the performance of the Q-Learning dynamic as measured by the Time Averaged Social Welfare, and comparing this with the Social Welfare achieved by the equilibrium. We provide a sufficient condition whereby the Q-Learning dynamic will outperform the equilibrium even if the dynamics do not converge.

cs.GT↗

arXiv2022

Argumentative Reward Learning: Reasoning About Human Preferences

We define a novel neuro-symbolic framework, argumentative reward learning, which combines preference-based argumentation with existing approaches to reinforcement learning from human feedback. Our method improves prior work by generalising human preferences, reducing the burden on the user and increasing the robustness of the reward model. We demonstrate this with a number of experiments.

cs.AI↗

arXiv2022

Program Semantics and a Verification Technique for Knowledge-Based Multi-Agent Systems

We give a relational and a weakest precondition semantics for "knowledge-based programs", i.e., programs that restrict observability of variables so as to richly express changes in the knowledge of agents who can or cannot observe said variables. Based on these knowledge-based programs, we define a program-epistemic logic to model complex epistemic properties of the execution of multi-agent systems. We translate the validity of program-epistemic logic formulae into first-order validity, using our weakest precondition semantics and an ingenious book-keeping of variable assignment. We implement our translation in Haskell in a general way (i.e., independently of the programs in the logical statements), and test this novel verification method for our new program-epistemic logic on a series of well-established examples.

cs.LO↗

arXiv2022

A Sahlqvist-style Correspondence Theorem for Linear-time Temporal Logic

The language of modal logic is capable of expressing first-order conditions on Kripke frames. The classic result by Henrik Sahlqvist identifies a significant class of modal formulas for which first-order conditions -- or Sahlqvist correspondents -- can be find in an effective, algorithmic way. Recent works have successfully extended this classic result to more complex modal languages. In this paper, we pursue a similar line and develop a Sahlqvist-style correspondence theorem for Linear-time Temporal Logic (LTL), which is one of the most widely used formal languages for temporal specification. LTL extends the syntax of basic modal logic with dedicated temporal operators Next X and Until U . As a result, the complexity of the class of formulas that have first-order correspondents also increases accordingly. In this paper, we identify a significant class of LTL Sahlqvist formulas built by using modal operators F , G, X, and U . The main result of this paper is to prove the correspondence of LTL Sahlqvist formulas to frame conditions that are definable in first-order language.

cs.LO↗