We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of \emph{all} actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is $\tilde{O}(\sigma^{-1}_{\min} s_{\star} H \sqrt{N})$, where $\sigma_{\min}$ denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, $s_\star$ is the sparsity parameter, $H$ is the length of an episode, and $N$ is the number of rounds. We provide a lower regret bound that matches the upper bound up to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.

我们提出了一种新的遗憾最小化算法，用于具有稀疏线性马尔可夫决策过程（SMDP）的情节性问题，其中状态转移分布是观察特征的线性函数。

稀疏强化学习的双重稳健方法