MetaCURL: Non-stationary Concave Utility Reinforcement Learning
Bianca Marin Moreno, Margaux Brégère, Pierre Gaillard, Nadia Oudjane
TL;DR
MetaCURL tackles online Concave Utility Reinforcement Learning in non-stationary episodic MDPs by combining multiple baseline CURL algorithms across intervals with a sleeping-expert meta-aggregation. It introduces a two-layer estimator for the unknown, time-varying transition kernel $p^t$ and uses LEA/EWA to adaptively weight the interval-based learners without prior knowledge of when changes occur. The main theoretical contribution is a near-optimal dynamic regret bound of the form $ ilde{O}ig( oot 2 ext{ of }{ ext{(terms)}}ig)$, specifically $\tilde{O}( \sqrt{\Delta^{\pi^*} T} + \min\{\sqrt{T \Delta^p_\infty}, \; T^{2/3} (\Delta^p)^{1/3}\})$, valid under partial information about $p^t$ and adversarial $F^t$. The approach yields the first dynamic-regret analysis for a CURL method in non-stationary MDPs and offers a scalable, parameter-free framework that can serve as a baseline for future RL methods handling non-stationarity with full exploration. Overall, MetaCURL provides a principled, efficient path to robust CURL in changing environments with broad applicability to RL under adversarial dynamics.
Abstract
We explore online learning in episodic loop-free Markov decision processes on non-stationary environments (changing losses and probability transitions). Our focus is on the Concave Utility Reinforcement Learning problem (CURL), an extension of classical RL for handling convex performance criteria in state-action distributions induced by agent policies. While various machine learning problems can be written as CURL, its non-linearity invalidates traditional Bellman equations. Despite recent solutions to classical CURL, none address non-stationary MDPs. This paper introduces MetaCURL, the first CURL algorithm for non-stationary MDPs. It employs a meta-algorithm running multiple black-box algorithms instances over different intervals, aggregating outputs via a sleeping expert framework. The key hurdle is partial information due to MDP uncertainty. Under partial information on the probability transitions (uncertainty and non-stationarity coming only from external noise, independent of agent state-action pairs), we achieve optimal dynamic regret without prior knowledge of MDP changes. Unlike approaches for RL, MetaCURL handles full adversarial losses, not just stochastic ones. We believe our approach for managing non-stationarity with experts can be of interest to the RL community.