Average Reward Reinforcement Learning for Omega-Regular and Mean-Payoff Objectives (2505.15693v1)

Abstract: Recent advances in reinforcement learning (RL) have renewed focus on the design of reward functions that shape agent behavior. Manually designing reward functions is tedious and error-prone. A principled alternative is to specify behaviors in a formal language that can be automatically translated into rewards. Omega-regular languages are a natural choice for this purpose, given their established role in formal verification and synthesis. However, existing methods using omega-regular specifications typically rely on discounted reward RL in episodic settings, with periodic resets. This setup misaligns 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 focus on absolute liveness specifications -- a subclass of omega-regular languages that cannot be violated by any finite behavior prefix, making them well-suited to the continuing setting. We present the first model-free RL framework that translates absolute liveness specifications to average-reward objectives. Our approach enables learning in communicating MDPs without episodic resetting. We also introduce a reward structure for lexicographic multi-objective optimization, aiming to maximize an external average-reward objective among the policies that also maximize the satisfaction probability of a given 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 show our average-reward approach in continuing setting outperforms discount-based methods across benchmarks.

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

The paper "Average-Reward Reinforcement Learning for Omega-Regular and Mean-Payoff Objectives" by Kazemi et al. investigates the reinforcement learning (RL) paradigm in the context of continuing tasks with potentially infinite-horizon objectives. By addressing model-free RL design for communicating Markov Decision Processes (MDPs), the paper aims to translate omega-regular and mean-payoff specifications into average-reward objectives.

This paper acknowledges the limitations of the discounted-reward criterion, especially when applied to infinite behavior traces typical of omega-regular specifications. The discounted setting necessitates episodic resets that can misalign with these specifications. Instead, the authors focus on the average-reward criterion within the continuing setting of RL, providing a more suitable framework for situations requiring uninterrupted interaction over a single lifetime.

The research introduces absolute liveness specifications, a subclass of omega-regular languages, which are particularly aligned with the continuing task setting as they cannot be violated by any finite behavior prefix. This approach enables the conversion of omega-regular language specifications into average-reward objectives, thus facilitating learning in communicating MDPs without episodic resets.

One of the key contributions of the paper is the development of a model-free RL framework and reward structure that addresses lexicographic multi-objective optimization. This optimization entails maximizing an external average-reward objective while simultaneously maximizing the satisfaction probability of a given omega-regular specification. Importantly, the proposed method guarantees convergence even in unknown communicating MDPs, achieving this without requiring full knowledge of the environment—allowing for a truly model-free learning approach.

The empirical results demonstrate that the average-reward approach in the continuing setting significantly outperforms traditional discount-based methods across diverse benchmarks. The implications of these findings are substantial; they suggest that average-reward RL is a viable and more efficient alternative for domains characterized by infinite interaction sequences, such as autonomous monitoring or industrial process control.

Moreover, the paper speculates on the theoretical advancements this method offers—expanding the understanding and application of RL within tasks that require adherence to logical specifications over infinite traces. Future developments in AI could advance further by building upon the analytical framework provided here, particularly in more complex and realistic environments where continuous engagement without episodic interruptions is critical.

In extending these results, the paper also emphasizes the utility of their approach in lexicographic settings, addressing multiple objectives and proposing a theoretical basis for solving multi-objective optimization using average-reward RL. The robustness against the changing nature of goals and constraints in real-world applications is highlighted, with a focus on achieving equilibrium between external reward optimization and logical specification satisfaction.

Overall, Kazemi et al.'s research represents a significant step towards broadening the scope and applicability of reinforcement learning in environments where ongoing interactions are essential, and further developments in this area hold the potential to innovate and refine AI methodologies in practice.