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

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 benchmarks.

This paper investigated low-rank MDPs on both computation and sample complexities. It first introduced an $\mathsf{SL}$-oracle complexity framework and showed that many existing sample-efficient methods rely on planning or constrained planning oracles that are difficult to implement. Then, the paper proposed an optimistic actor-critic algorithm that requires only policy evaluation, which can be efficiently reduced to supervised learning, while achieving state-of-the-art sample complexity. This work also showed that approximate low-rank MDPs form a rich and expressive class via a conditional random Fourier feature construction. Empirically, the proposed method performs competitively against a strong baseline on standard benchmarks. Overall, this work demonstrates that strong theoretical guarantees and practical implementability can be achieved simultaneously in (approximate) low-rank MDPs.