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.\footnote{Our code is available at \url{https://github.com/hmishfaq/LMC-LSVI}}
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Posterior sampling with delayed feedback for reinforcement learning with linear function approximation
Recent studies in reinforcement learning (RL) have made significant progress by leveraging function approximation to alleviate the sample complexity hurdle for better performance. Despite the success, existing provably efficient algorithms typically rely on the accessibility of immediate feedback upon taking actions. The failure to account for the impact of delay in observations can significantly degrade the performance of real-world systems due to the regret blow-up. In this work, we tackle the challenge of delayed feedback in RL with linear function approximation by employing posterior sampling, which has been shown to empirically outperform the popular UCB algorithms in a wide range of regimes. We first introduce Delayed-PSVI, an optimistic value-based algorithm that effectively explores the value function space via noise perturbation with posterior sampling. We provide the first analysis for posterior sampling algorithms with delayed feedback in RL and show our algorithm achieves $\widetilde{O}(\sqrt{d^3H^3 T} + d^2H^2 E[\tau])$ worst-case regret in the presence of unknown stochastic delays. Here $E[\tau]$ is the expected delay. To further improve its computational efficiency and to expand its applicability in high-dimensional RL problems, we incorporate a gradient-based approximate sampling scheme via Langevin dynamics for Delayed-LPSVI, which maintains the same order-optimal regret guarantee with $\widetilde{O}(dHK)$ computational cost. Empirical evaluations are performed to demonstrate the statistical and computational efficacy of our algorithms.
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- PAR ID:
- 10558124
- Publisher / Repository:
- NeurIPS 2023
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 36
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 6782--6824
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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