Many real-world applications, such as those in medical domains, recommendation systems, etc, can be formulated as large state space reinforcement learning problems with only a small budget of the number of policy changes, i.e., low switching cost. This paper focuses on the linear Markov Decision Process (MDP) recently studied in Yang and Wang [2019a], Jin et al. [2019] where the linear function approximation is used for generalization on the large state space. We present the first algorithm for linear MDP with a low switching cost. Our algorithm achieves an ‹ O Ä√ d 3 H 4 K ä regret bound with a near-optimal O (dH log K) global switching cost where d is the feature dimension, H is the planning horizon and K is the number of episodes the agent plays. Our regret bound matches the best existing polynomial algorithm by and our switching cost is exponentially smaller than theirs. When specialized to tabular MDP, our switching cost bound improves those in Bai et al. [2019], Zhang et al. [2020b. We complement our positive result with an Ω (dH/ log d) global switching cost lower bound for any no-regret algorithm.

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