A Contraction Approach to Model-based Reinforcement Learning
This work provides theoretical insights for researchers in reinforcement learning, though it appears incremental as it builds on existing contraction methods without introducing a new paradigm.
The paper tackles the lack of theoretical understanding in Model-based Reinforcement Learning by analyzing cumulative reward error using a contraction approach for continuous state and action spaces, proving that branched rollouts reduce error and are essential for deterministic transitions to achieve Bellman contraction.
Despite its experimental success, Model-based Reinforcement Learning still lacks a complete theoretical understanding. To this end, we analyze the error in the cumulative reward using a contraction approach. We consider both stochastic and deterministic state transitions for continuous (non-discrete) state and action spaces. This approach doesn't require strong assumptions and can recover the typical quadratic error to the horizon. We prove that branched rollouts can reduce this error and are essential for deterministic transitions to have a Bellman contraction. Our analysis of policy mismatch error also applies to Imitation Learning. In this case, we show that GAN-type learning has an advantage over Behavioral Cloning when its discriminator is well-trained.