Real-world reinforcement learning (RL) applications often come with possibly infinite state and action space, and in such a situation classical RL algorithms developed in the tabular setting are not applicable anymore. A popular approach to overcoming this issue is by applying function approximation techniques to the underlying structures of the Markovdecision processes (MDPs).

Real-world reinforcement learning (RL) applications often come with possibly infinite state and action space, and in such a situation classical RL algorithms developed in the tabular setting are not applicable anymore. A popular approach to overcoming this issue is by applying function approximation techniques to the underlying structures of the Markovdecision processes (MDPs).

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 \citep{jin2020provably}, 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.

Real-world reinforcement learning (RL) applications often come with possibly infinite state and action space, and in such a situation classical RL algorithms developed in the tabular setting are not applicable anymore. A popular approach to overcoming this issue is by applying function approximation techniques to the underlying structures of the Markov decision processes (MDPs).

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 algorithms achieve the same regret as the LSVI-UCB algorithm \citep{jin2020provably}, 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.

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.