用深度生成模型和广义贝叶斯方法,提升强化学习在不确定环境中的决策能力。
Generalized Bayesian deep reinforcement learning
- 用预序评分规则构建无似然函数的贝叶斯后验,结合SMC采样器
- 提出期望汤普森采样(ETS),利用后验分布均值优化策略,性能优于传统方法
- 适用于高维参数空间的强化学习,支持离散与连续动作空间
贝叶斯强化学习(BRL)融合贝叶斯统计与强化学习,在不确定性环境中做出最优决策。作为基于模型的强化学习方法,其核心包含两个部分:(1) 从数据中推断环境动态模型的后验分布;(2) 基于该后验进行策略学习。本文通过深度生成模型建模未知环境动态,假设马尔可夫依赖关系。由于缺乏显式似然函数,采用广义预测-序列(预序)评分规则(SR)后验进行训练。使用序列蒙特卡洛(SMC)采样器从该广义贝叶斯后验中抽样,并引入基于梯度的马尔可夫核以提升高维神经网络参数空间的可扩展性。为证明预序评分规则后验的有效性,给出了类似伯恩斯坦-冯米塞斯的收敛定理。策略学习方面,提出期望汤普森采样(ETS),通过最大化后验分布下的期望价值函数来学习最优策略,优于仅使用单个后验样本的传统汤普森采样及其扩展。该方法在离散动作空间下进行了理论分析与模拟研究。最后,将框架成功拓展至连续动作空间的复杂问题,虽未提供理论保证,但实验表现良好。
原文摘要 · Abstract (English)
Bayesian reinforcement learning (BRL) is a method that merges principles from Bayesian statistics and reinforcement learning to make optimal decisions in uncertain environments. As a model-based RL method, it has two key components: (1) inferring the posterior distribution of the model for the data-generating process (DGP) and (2) policy learning using the learned posterior. We propose to model the dynamics of the unknown environment through deep generative models, assuming Markov dependence. In the absence of likelihood functions for these models, we train them by learning a generalized predictive-sequential (or prequential) scoring rule (SR) posterior. We used sequential Monte Carlo (SMC) samplers to draw samples from this generalized Bayesian posterior distribution. In conjunction, to achieve scalability in the high-dimensional parameter space of the neural networks, we use the gradient-based Markov kernels within SMC. To justify the use of the prequential scoring rule posterior, we prove a Bernstein-von Mises-type theorem. For policy learning, we propose expected Thompson sampling (ETS) to learn the optimal policy by maximising the expected value function with respect to the posterior distribution. This improves upon traditional Thompson sampling (TS) and its extensions, which utilize only one sample drawn from the posterior distribution. This improvement is studied both theoretically and using simulation studies, assuming a discrete action space. Finally, we successfully extended our setup for a challenging problem with a continuous action space without theoretical guarantees.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。