Author name cluster

Mateo Perez

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8 papers

2 author rows

JAIR Journal 2026 Journal Article

Average Reward Reinforcement Learning for Omega-Regular and Mean-Payoff Objectives

Milad Kazemi
Mateo Perez
Fabio Somenzi
Sadegh Soudjani
Ashutosh Trivedi
Alvaro Velasquez

Recent advances in reinforcement learning (RL) have renewed focus on the design of reward functions that shape agent behavior. Manually crafting such functions is often tedious and error-prone. A more principled alternative is to specify behavioral requirements using a formal, unambiguous language that can be automatically translated into a reward function. Omega-regular languages are a natural choice for this purpose, given their established role in formal verification and synthesis. However, existing approaches using omega-regular specifications typically rely on discounted reward RL in an episodic setting, where the environment is periodically reset to an initial state during learning. This setup is misaligned with the semantics of omega-regular specifications, which describe properties over infinite behavior traces. In such cases, the average reward criterion and the continuing setting—where the agent interacts with the environment over a single, uninterrupted lifetime—are more appropriate. To address the challenges of infinite-horizon, continuing tasks, we restrict our focus to the subclass of omega-regular languages known as absolute liveness specifications. These specifications cannot be violated by any finite prefix of the agent’s behavior, aligning naturally with the continuing setting. We present the first model-free RL framework that translates absolute liveness specifications to average-reward objectives. In contrast to prior work, our approach enables learning in communicating Markov Decision Processes without episodic resetting. We further introduce a reward structure for lexicographic multi-objective optimization, where the goal is to maximize an external average-reward objective among the policies that also maximize the satisfaction probability of a given absolute liveness omega-regular specification. Our method guarantees convergence in unknown communicating MDPs and supports on-the-fly reductions that do not require full knowledge of the environment, thus enabling model-free RL. Empirical results across various benchmarks demonstrate that our average-reward approach in the continuing setting is more effective than competing methods based on discounting.

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AAAI Conference 2024 Conference Paper

A PAC Learning Algorithm for LTL and Omega-Regular Objectives in MDPs

Mateo Perez
Fabio Somenzi
Ashutosh Trivedi

Linear temporal logic (LTL) and omega-regular objectives---a superset of LTL---have seen recent use as a way to express non-Markovian objectives in reinforcement learning. We introduce a model-based probably approximately correct (PAC) learning algorithm for omega-regular objectives in Markov decision processes (MDPs). As part of the development of our algorithm, we introduce the epsilon-recurrence time: a measure of the speed at which a policy converges to the satisfaction of the omega-regular objective in the limit. We prove that our algorithm only requires a polynomial number of samples in the relevant parameters, and perform experiments which confirm our theory.

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AAAI Conference 2024 Conference Paper

Assume-Guarantee Reinforcement Learning

Milad Kazemi
Mateo Perez
Fabio Somenzi
Sadegh Soudjani
Ashutosh Trivedi
Alvaro Velasquez

We present a modular approach to reinforcement learning (RL) in environments consisting of simpler components evolving in parallel. A monolithic view of such modular environments may be prohibitively large to learn, or may require unrealizable communication between the components in the form of a centralized controller. Our proposed approach is based on the assume-guarantee paradigm where the optimal control for the individual components is synthesized in isolation by making assumptions about the behaviors of neighboring components, and providing guarantees about their own behavior. We express these assume-guarantee contracts as regular languages and provide automatic translations to scalar rewards to be used in RL. By combining local probabilities of satisfaction for each component, we provide a lower bound on the probability of satisfaction of the complete system. By solving a Markov game for each component, RL can produce a controller for each component that maximizes this lower bound. The controller utilizes the information it receives through communication, observations, and any knowledge of a coarse model of other agents. We experimentally demonstrate the efficiency of the proposed approach on a variety of case studies.

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ECAI Conference 2024 Conference Paper

Multi-Agent Reinforcement Learning for Alternating-Time Logic

Ernst Moritz Hahn
Mateo Perez
Sven Schewe
Fabio Somenzi
Ashutosh Trivedi 0001
Dominik Wojtczak

Alternating-time temporal logic (ATL) extends branching time logic by enabling quantification over paths that result from the strategic choices made by multiple agents in various coalitions within the system. While classical temporal logics express properties of “closed” systems, ATL can express properties of “open” systems resulting from interactions among several agents. Reinforcement learning (RL) is a sampling-based approach to decision-making where learning agents, guided by a scalar reward function, discover optimal policies through repeated interactions with the environment. The challenge of translating high-level objectives into scalar rewards for RL has garnered increased interest, particularly following the success of model-free RL algorithms. This paper presents an approach for deploying model-free RL to verify multi-agent systems against ATL specifications. The key contribution of this paper is a verification procedure for model-free RL of quantitative and non-nested classic ATL properties, based on Q-learning, demonstrated on a natural subclass of non-nested ATL formulas.

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AAAI Conference 2024 Conference Paper

Omega-Regular Decision Processes

Ernst Moritz Hahn
Mateo Perez
Sven Schewe
Fabio Somenzi
Ashutosh Trivedi
Dominik Wojtczak

Regular decision processes (RDPs) are a subclass of non-Markovian decision processes where the transition and reward functions are guarded by some regular property of the past (a lookback). While RDPs enable intuitive and succinct representation of non-Markovian decision processes, their expressive power coincides with finite-state Markov decision processes (MDPs). We introduce omega-regular decision processes (ODPs) where the non-Markovian aspect of the transition and reward functions are extended to an omega-regular lookahead over the system evolution. Semantically, these lookaheads can be considered as promises made by the decision maker or the learning agent about her future behavior. In particular, we assume that, if the promised lookaheads are not met, then the payoff to the decision maker is falsum (least desirable payoff), overriding any rewards collected by the decision maker. We enable optimization and learning for ODPs under the discounted-reward objective by reducing them to lexicographic optimization and learning over finite MDPs. We present experimental results demonstrating the effectiveness of the proposed reduction.

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ECAI Conference 2023 Conference Paper

Omega-Regular Reward Machines

Ernst Moritz Hahn
Mateo Perez
Sven Schewe
Fabio Somenzi
Ashutosh Trivedi 0001
Dominik Wojtczak

Reinforcement learning (RL) is a powerful approach for training agents to perform tasks, but designing an appropriate reward mechanism is critical to its success. However, in many cases, the complexity of the learning objectives goes beyond the capabilities of the Markovian assumption, necessitating a more sophisticated reward mechanism. Reward machines and ω-regular languages are two formalisms used to express non-Markovian rewards for quantitative and qualitative objectives, respectively. This paper introduces ω-regular reward machines, which integrate reward machines with ω-regular languages to enable an expressive and effective reward mechanism for RL. We present a model-free RL algorithm to compute ε-optimal strategies against ω-regular reward machines and evaluate the effectiveness of the proposed algorithm through experiments.

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NeurIPS Conference 2022 Conference Paper

Recursive Reinforcement Learning

Ernst Moritz Hahn
Mateo Perez
Sven Schewe
Fabio Somenzi
Ashutosh Trivedi
Dominik Wojtczak

Recursion is the fundamental paradigm to finitely describe potentially infinite objects. As state-of-the-art reinforcement learning (RL) algorithms cannot directly reason about recursion, they must rely on the practitioner's ingenuity in designing a suitable "flat" representation of the environment. The resulting manual feature constructions and approximations are cumbersome and error-prone; their lack of transparency hampers scalability. To overcome these challenges, we develop RL algorithms capable of computing optimal policies in environments described as a collection of Markov decision processes (MDPs) that can recursively invoke one another. Each constituent MDP is characterized by several entry and exit points that correspond to input and output values of these invocations. These recursive MDPs (or RMDPs) are expressively equivalent to probabilistic pushdown systems (with call-stack playing the role of the pushdown stack), and can model probabilistic programs with recursive procedural calls. We introduce Recursive Q-learning---a model-free RL algorithm for RMDPs---and prove that it converges for finite, single-exit and deterministic multi-exit RMDPs under mild assumptions.

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AAMAS Conference 2022 Conference Paper

Translating Omega-Regular Specifications to Average Objectives for Model-Free Reinforcement Learning

Milad Kazemi
Mateo Perez
Fabio Somenzi
Sadegh Soudjani
Ashutosh Trivedi
Alvaro Velasquez

Recent success in reinforcement learning (RL) has brought renewed attention to the design of reward functions by which agent behavior is reinforced or deterred. Manually designing reward functions is tedious and error-prone. An alternative approach is to specify a formal, unambiguous logic requirement, which is automatically translated into a reward function to be learned from. Omega-regular languages, of which Linear Temporal Logic (LTL) is a subset, are a natural choice for specifying such requirements due to their use in verification and synthesis. However, current techniques based on omega-regular languages learn in an episodic manner whereby the environment is periodically reset to an initial state during learning. In some settings, this assumption is challenging or impossible to satisfy. Instead, in the continuing setting the agent explores the environment without resets over a single lifetime. This is a more natural setting for reasoning about omega-regular specifications defined over infinite traces of agent behavior. Optimizing the average reward instead of the usual discounted reward is more natural in this case due to the infinite-horizon objective that poses challenges to the convergence of discounted RL solutions. We restrict our attention to the omega-regular languages which correspond to absolute liveness specifications. These specifications cannot be invalidated by any finite prefix of agent behavior, in accordance with the spirit of a continuing problem. We propose a translation from absolute liveness omega-regular languages to an average reward objective for RL. Our reduction can be done on-thefly, without full knowledge of the environment, thereby enabling the use of model-free RL algorithms. Additionally, we propose a reward structure that enables RL without episodic resetting in communicating MDPs, unlike previous approaches. We demonstrate empirically with various benchmarks that our proposed method of using average reward RL for continuing tasks defined by omegaregular specifications is more effective than competing approaches that leverage discounted RL.

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