Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo (2305.18246v2)

Abstract: 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.

• The paper introduces LMC-LSVI, an algorithm that uses noisy gradient descent to sample the exact Q-value posterior in reinforcement learning.
• It achieves a sublinear regret bound of approximately O(d^(3/2)H^(3/2)√T) in linear MDPs, positioning it among top randomized algorithms.
• The study extends the approach to deep RL with Adam LMCDQN, demonstrating competitive performance on benchmarks like Atari57 in both dense and sparse reward settings.

Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo

The paper "Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo" presents an in-depth exploration of a novel method in reinforcement learning (RL) intended to address the fundamental challenge of balancing exploration and exploitation. The authors explore a strategy leveraging Langevin Monte Carlo (LMC) for sampling the Q function from its posterior distribution, circumventing the limitations associated with Gaussian approximations typically employed in existing Thompson sampling algorithms.

The paper's primary contribution is the introduction of the Langevin Monte Carlo Least-Squares Value Iteration (LMC-LSVI) algorithm, which stands out by efficiently performing noisy gradient descent updates. This methodology enables the learning of the exact posterior distribution of the Q function, facilitating its integration within deep RL contexts, particularly with high-dimensional tasks. A significant achievement of the LMC-LSVI is its sublinear regret bound of $\tilde{O}(d^{3/2}H^{3/2}\sqrt{T})$ in linear MDP settings, where $d$ is the feature dimension, $H$ is the planning horizon, and $T$ denotes the total steps. This regret bound positions LMC-LSVI among the best in class across known randomized algorithms.

In addition to theoretical insights, the paper extends its approach to a practical implementation tailored for deep RL, known as the Adam Langevin Monte Carlo Deep Q-Network (Adam LMCDQN). This variant employs the Adam optimizer to tackle pathological curvature and saddle points in optimization landscapes, thereby enhancing the method's applicability in complex environments, such as those found in the Atari57 suite.

The empirical evaluation provides robust evidence of Adam LMCDQN achieving comparable or superior results against leading exploration strategies in deep RL, showcasing its potential as a well-rounded solution bridging theoretical rigor and practical performance. The exploration tasks, such as the Atari benchmarks, illustrate Adam LMCDQN's capability to maintain competitive performance across both dense and sparse reward environments, reflecting its adeptness at conducting deep exploration efficiently.

The implications of this research are multifaceted. On a theoretical level, it advances our understanding of posterior sampling techniques within RL, particularly highlighting the potential of LMC to offer principled, scalable solutions. Practically, it posits a versatile tool in Adam LMCDQN for real-world applications, enabling practitioners to harness deep RL models while maintaining exploration efficacy through model uncertainty quantification.

Future research could enrich these findings by addressing the current gap in understanding the discrepancy in regret bounds between UCB and Thompson sampling-based methods, potentially leading to even tighter bounds for LMC-LSVI. Further, extending LMC-based strategies to more challenging continuous control tasks and other RL settings could unlock new capabilities for efficient exploration across various application domains in artificial intelligence.