Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints
This work addresses efficiency in RL for scenarios with limited adaptivity, such as batch or rare-switch settings, offering provable guarantees that are incremental improvements over prior methods.
The paper tackles reinforcement learning with linear function approximation under adaptivity constraints, proposing algorithms for batch learning and rare policy switch models that achieve regret bounds matching existing methods while using significantly fewer batches or policy switches, with concrete bounds like $ ilde O(\sqrt{d^3H^3T})$ requiring only $\sqrt{T/dH}$ batches.
We study reinforcement learning (RL) with linear function approximation under the adaptivity constraint. We consider two popular limited adaptivity models: the batch learning model and the rare policy switch model, and propose two efficient online RL algorithms for episodic linear Markov decision processes, where the transition probability and the reward function can be represented as a linear function of some known feature mapping. 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. We also establish a lower bound for the batch learning model, which suggests that the dependency on $B$ in our regret bound is tight.