We study query and computationally efficient planning algorithms with linear function approximation and a simulator. We assume that the agent only has local access to the simulator, meaning that the agent can only query the simulator at states that have been visited before. This setting is more practical than many prior works on reinforcement learning with a generative model. We propose an algorithm named confident Monte Carlo least square policy iteration (Confident MC-LSPI) for this setting. Under the assumption that the Q-functions of all deterministic policies are linear in known features of the state-action pairs, we show that our algorithm has polynomial query and computational complexities in the dimension of the features, the effective planning horizon and the targeted sub-optimality, while these complexities are independent of the size of the state space. One technical contribution of our work is the introduction of a novel proof technique that makes use of a virtual policy iteration algorithm. We use this method to leverage existing results on $\ell_\infty$-bounded approximate policy iteration to show that our algorithm can learn the optimal policy for the given initial state even only with local access to the simulator. We believe that this technique can be extended to broader settings beyond this work.

研究使用线性函数逼近和模拟器的查询和计算高效的计划算法，在这种情况下，我们提出了名为“Confident MC-LSPI”和“Confident MC-Politex”的两种算法，同时证明了我们的算法在特征，有效规划控制范围和目标次优性的维度中具有多项查询和计算成本，而这些成本与状态空间的大小无关。

使用线性函数逼近实现高效的本地规划