Planning in Markov Decision Processes with Gap-Dependent Sample Complexity
This addresses sample efficiency in reinforcement learning planning for researchers, though it appears incremental as it builds on existing trajectory-based methods with new guarantees.
The paper tackles the problem of planning in Markov Decision Processes by proposing MDP-GapE, a trajectory-based Monte-Carlo Tree Search algorithm, and proves a problem-dependent sample complexity bound expressed in terms of sub-optimality gaps, with experiments showing it is effective in practice.
We propose MDP-GapE, a new trajectory-based Monte-Carlo Tree Search algorithm for planning in a Markov Decision Process in which transitions have a finite support. We prove an upper bound on the number of calls to the generative models needed for MDP-GapE to identify a near-optimal action with high probability. This problem-dependent sample complexity result is expressed in terms of the sub-optimality gaps of the state-action pairs that are visited during exploration. Our experiments reveal that MDP-GapE is also effective in practice, in contrast with other algorithms with sample complexity guarantees in the fixed-confidence setting, that are mostly theoretical.