Planning in Markov Decision Processes with Gap-Dependent Sample Complexity

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 sampled trajectories needed for MDP-GapE to identify a near-optimal action with high probability. This problem-dependent 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.

Authors

• Anders Jonsson
• Emilie Kaufmann
• Pierre Menard
• Omar Darwiche Domingues
• Edouard Leurent
• Michal Valko INRIA Lille - Nord Europe

Keywords

No keywords are indexed for this paper.