Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo
This addresses the exploration problem in reinforcement learning for practitioners, offering a provably efficient and easy-to-deploy method, though it is incremental as it builds on Thompson sampling with a new sampling technique.
The paper tackles the inefficiency of Gaussian approximations in Thompson sampling for RL by introducing a scalable exploration strategy that samples Q-functions directly via Langevin Monte Carlo, achieving a regret bound of O~(d^{3/2}H^{3/2}√T) in linear MDPs and competitive results on Atari57 tasks.
We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algorithms is the need to perform a Gaussian approximation of the posterior distribution, which is not a good surrogate in most practical settings. We instead directly sample the Q function from its posterior distribution, by using Langevin Monte Carlo, an efficient type of Markov Chain Monte Carlo (MCMC) method. Our method only needs to perform noisy gradient descent updates to learn the exact posterior distribution of the Q function, which makes our approach easy to deploy in deep RL. We provide a rigorous theoretical analysis for the proposed method and demonstrate that, in the linear Markov decision process (linear MDP) setting, it has a regret bound of $\tilde{O}(d^{3/2}H^{3/2}\sqrt{T})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $T$ is the total number of steps. We apply this approach to deep RL, by using Adam optimizer to perform gradient updates. Our approach achieves better or similar results compared with state-of-the-art deep RL algorithms on several challenging exploration tasks from the Atari57 suite.