Going Beyond Linear RL: Sample Efficient Neural Function Approximation
This work addresses a foundational gap in reinforcement learning theory for researchers and practitioners, offering incremental theoretical advancements for nonlinear function approximation.
The paper tackles the lack of theoretical understanding for deep reinforcement learning with neural network Q-function approximations, providing sample-efficient algorithms for two-layer neural networks under completeness and realizability assumptions, with sample complexity scaling linearly in algebraic dimension and significant improvements over linear methods.
Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches, little is known about nonlinear RL with neural net approximations of the Q functions. This is the focus of this work, where we study function approximation with two-layer neural networks (considering both ReLU and polynomial activation functions). Our first result is a computationally and statistically efficient algorithm in the generative model setting under completeness for two-layer neural networks. Our second result considers this setting but under only realizability of the neural net function class. Here, assuming deterministic dynamics, the sample complexity scales linearly in the algebraic dimension. In all cases, our results significantly improve upon what can be attained with linear (or eluder dimension) methods.