Breaking the Computational Barrier: Provably Efficient Actor-Critic for Low-Rank MDPs

TL;DR

This paper introduces a provably efficient actor-critic algorithm for low-rank MDPs that leverages supervised learning for policy evaluation, improving computational and sample efficiency.

Contribution

It proposes a novel optimistic actor-critic method relying solely on the policy evaluation oracle, avoiding expensive planning or optimization.

Findings

Outperforms existing sample complexity guarantees for low-rank MDPs

Avoids computationally expensive planning oracles

Validated with experiments on standard Gym environments

Abstract

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL algorithms achieve favorable sample complexity, but often rely on computationally intractable oracles. In this paper, we use supervised learning as a computational proxy to establish a clear hierarchy of commonly adopted RL oracles under low-rank Markov Decision Processes (MDPs). This hierarchy shows that policy evaluation is the most computationally efficient oracle, provided that supervised learning can be efficiently solved. Motivated by this observation, we propose a novel optimistic actor-critic algorithm that relies solely on the policy evaluation oracle. We prove that our algorithm outperforms the existing sample complexity guarantees for low-rank MDPs while avoiding computationally expensive planning or optimization oracles commonly assumed in prior works. We further extend our theoretical results to approximately low-rank MDPs and demonstrate that this setting captures a broad class of real-world environments. Finally, we validate our theoretical results with experiments on several standard Gym environments.