Online Sub-Sampling for Reinforcement Learning with General Function Approximation

Designing provably efficient algorithms with general function approximation is an important open problem in reinforcement learning. Recently, Wang et al.~[2020c] establish a value-based algorithm with general function approximation that enjoys $\widetilde{O}(\mathrm{poly}(dH)\sqrt{K})$\footnote{Throughout the paper, we use $\widetilde{O}(\cdot)$ to suppress logarithm factors. } regret bound, where $d$ depends on the complexity of the function class, $H$ is the planning horizon, and $K$ is the total number of episodes. However, their algorithm requires $\Omega(K)$ computation time per round, rendering the algorithm inefficient for practical use. In this paper, by applying online sub-sampling techniques, we develop an algorithm that takes $\widetilde{O}(\mathrm{poly}(dH))$ computation time per round on average, and enjoys nearly the same regret bound. Furthermore, the algorithm achieves low switching cost, i.e., it changes the policy only $\widetilde{O}(\mathrm{poly}(dH))$ times during its execution, making it appealing to be implemented in real-life scenarios. Moreover, by using an upper-confidence based exploration-driven reward function, the algorithm provably explores the environment in the reward-free setting. In particular, after $\widetilde{O}(\mathrm{poly}(dH))/\epsilon^2$ rounds of exploration, the algorithm outputs an $\epsilon$-optimal policy for any given reward function