We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning (RL). When the state space is large or continuous, traditional tabular approaches are unfeasible and some form of function approximation is mandatory. In this paper, we introduce an optimistically-initialized variant of the popular randomized least-squares value iteration (RLSVI), a model-free algorithm where exploration is induced by perturbing the least-squares approximation of the action-value function. Under the assumption that the Markov decision process has low-rank transition dynamics, we prove that the frequentist regret of RLSVI is upper-bounded by $\widetilde O(d^2 H^2 \sqrt{T})$ where $ d $ are the feature dimension, $ H $ is the horizon, and $ T $ is the total number of steps. To the best of our knowledge, this is the first frequentist regret analysis for randomized exploration with function approximation.

翻译：我们考虑有限水平强化学习（RL）中的探索-利用困境。当状态空间很大或连续时，传统的表格方法不可行，因此必须使用某种形式的函数近似。在本文中，我们引入了流行的随机化最小二乘值迭代（RLSVI）的一种乐观初始化变体，这是一种无模型算法，通过扰动动作值函数的最小二乘近似来诱导探索。在马尔可夫决策过程具有低秩转移动态的假设下，我们证明RLSVI的频率遗憾上界为$\widetilde O(d^2 H^2 \sqrt{T})$，其中$ d $是特征维度，$ H $是水平长度，$ T $是总步数。据我们所知，这是首次对带有函数近似的随机化探索进行频率遗憾分析。