Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints

We study reinforcement learning (RL) with linear function approximation under the adaptivity constraint. We consider two popular limited adaptivity models: batch learning model and rare policy switch model, and propose two efficient online RL algorithms for linear Markov decision processes. In specific, for the batch learning model, our proposed LSVI-UCB-Batch algorithm achieves an $\tilde O(\sqrt{d^3H^3T} + dHT/B)$ regret, where $d$ is the dimension of the feature mapping, $H$ is the episode length, $T$ is the number of interactions and $B$ is the number of batches. Our result suggests that it suffices to use only $\sqrt{T/dH}$ batches to obtain $\tilde O(\sqrt{d^3H^3T})$ regret. For the rare policy switch model, our proposed LSVI-UCB-RareSwitch algorithm enjoys an $\tilde O(\sqrt{d^3H^3T[1+T/(dH)]^{dH/B}})$ regret, which implies that $dH\log T$ policy switches suffice to obtain the $\tilde O(\sqrt{d^3H^3T})$ regret. Our algorithms achieve the same regret as the LSVI-UCB algorithm (Jin et al., 2019), yet with a substantially smaller amount of adaptivity.