On the Generalization Gap in Reparameterizable Reinforcement Learning
This work addresses the challenge of generalization in RL for researchers, providing theoretical insights and empirical validation, though it is incremental as it builds on existing supervised learning theory.
The paper tackled the generalization gap in reparameterizable reinforcement learning by deriving theoretical bounds on the difference between expected and empirical returns, relating it to factors like environment smoothness, and empirically verifying these relationships through simulations.
Understanding generalization in reinforcement learning (RL) is a significant challenge, as many common assumptions of traditional supervised learning theory do not apply. We focus on the special class of reparameterizable RL problems, where the trajectory distribution can be decomposed using the reparametrization trick. For this problem class, estimating the expected return is efficient and the trajectory can be computed deterministically given peripheral random variables, which enables us to study reparametrizable RL using supervised learning and transfer learning theory. Through these relationships, we derive guarantees on the gap between the expected and empirical return for both intrinsic and external errors, based on Rademacher complexity as well as the PAC-Bayes bound. Our bound suggests the generalization capability of reparameterizable RL is related to multiple factors including "smoothness" of the environment transition, reward and agent policy function class. We also empirically verify the relationship between the generalization gap and these factors through simulations.