Breaking the Computational Barrier: Provably Efficient Actor-Critic for Low-Rank MDPs
It addresses the computational bottleneck in RL with function approximation by establishing a hierarchy of oracles and providing a provably efficient algorithm for low-rank MDPs.
The paper proposes a novel optimistic actor-critic algorithm for low-rank MDPs that uses only a policy evaluation oracle, achieving improved sample complexity over prior methods while avoiding computationally expensive oracles. The algorithm is validated on standard Gym environments.
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.