已知观测模型下,高效学习平均奖励的部分可观测强化学习问题。
Efficient Learning of POMDPs with Known Observation Model in Average-Reward Setting
- 基于信念策略采样,利用观测感知谱估计法学习未知转移模型。
- 算法实现$ ext{O}( ext{sqrt}{T ext{log}(T)})$的累积后悔上界。
- 适合高维状态、动作与观测空间下的在线决策任务。
在无限时域平均奖励设定下,处理部分可观测马尔可夫决策过程(POMDP)是一项挑战性任务。本文假设已知观测模型但未知转移模型,提出观测感知谱(OAS)估计方法,可从信念策略生成的样本中学习POMDP参数。进一步设计了OAS-UCRL算法,通过递增长度的多轮迭代,每轮基于当前模型估计更新最优信念策略并收集新样本。该算法遵循“不确定性中的乐观”原则,隐式平衡探索与利用。我们证明了OAS估计的一致性,并建立了算法$ ext{O}( ext{sqrt}{T ext{log}(T)})$的后悔上界。实验表明,该方法在状态、动作与观测空间维度较高时仍具高效性,优于多个基线方法。
原文摘要 · Abstract (English)
Dealing with Partially Observable Markov Decision Processes is notably a challenging task. We face an average-reward infinite-horizon POMDP setting with an unknown transition model, where we assume the knowledge of the observation model. Under this assumption, we propose the Observation-Aware Spectral (OAS) estimation technique, which enables the POMDP parameters to be learned from samples collected using a belief-based policy. Then, we propose the OAS-UCRL algorithm that implicitly balances the exploration-exploitation trade-off following the $\textit{optimism in the face of uncertainty}$ principle. The algorithm runs through episodes of increasing length. For each episode, the optimal belief-based policy of the estimated POMDP interacts with the environment and collects samples that will be used in the next episode by the OAS estimation procedure to compute a new estimate of the POMDP parameters. Given the estimated model, an optimization oracle computes the new optimal policy. We show the consistency of the OAS procedure, and we prove a regret guarantee of order $\mathcal{O}(\sqrt{T \log(T)})$ for the proposed OAS-UCRL algorithm. We compare against the oracle playing the optimal stochastic belief-based policy and show the efficient scaling of our approach with respect to the dimensionality of the state, action, and observation space. We finally conduct numerical simulations to validate and compare the proposed technique with other baseline approaches.
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