Breaking the sample size barrier in model-based reinforcement learning with a generative model

We investigate the sample efficiency of reinforcement learning in a ?-discounted infinite-horizon Markov decision process (MDP) with state space S and action space A, assuming access to a generative model. Despite a number of prior work tackling this problem, a complete picture of the trade-offs between sample complexity and statistical accuracy is yet to be determined. In particular, prior results suffer from a sample size barrier, in the sense that their claimed statistical guarantees hold only when the sample size exceeds at least ₍₁^|S||A|_-?₎₂ (up to some log factor). The current paper overcomes this barrier by certifying the minimax optimality of model-based reinforcement learning as soon as the sample size exceeds the order of ^|S||A|_1-? (modulo some log factor). More specifically, a perturbed model-based planning algorithm provably finds an e-optimal policy with an order of ₍₁^|S||A|_-?_)3e2 log ₍₁^|S||A|_-?)_e samples for any e ? (0, _1-¹_? ]. Along the way, we derive improved (instance-dependent) guarantees for model-based policy evaluation. To the best of our knowledge, this work provides the first minimax-optimal guarantee in a generative model that accommodates the entire range of sample sizes (beyond which finding a meaningful policy is information theoretically impossible).