We study episodic reinforcement learning in non-stationary linear (a.k.a. low-rank) Markov Decision Processes (MDPs), i.e, both the reward and transition kernel are linear with respect to a given feature map and are allowed to evolve either slowly or abruptly over time. For this problem setting, we propose OPT-WLSVI an optimistic model-free algorithm based on weighted least squares value iteration which uses exponential weights to smoothly forget data that are far in the past. We show that our algorithm, when competing against the best policy at each time, achieves a regret that is upped bounded by $\widetilde{\mathcal{O}}(d^{7/6}H^2 \Delta^{1/3} K^{2/3})$ where $d$ is the dimension of the feature space, $H$ is the planning horizon, $K$ is the number of episodes and $\Delta$ is a suitable measure of non-stationarity of the MDP. This is the first regret bound for non-stationary reinforcement learning with linear function approximation.

本研究提出了一种基于权重最小二乘值迭代的非稳态线性马尔可夫决策过程（MDP）最优模型-free算法 OPT-WLSVI，使用指数权重平滑地遗忘过去的数据，与先前的研究相比解决了遗忘策略上的技术差距，并分析了与最佳策略竞争的总遗憾是有上限的。

非定常线性马尔可夫决策过程中的高效学习