Near-Optimal Reinforcement Learning with Multi-Step Transition Lookahead
Theorists prove multi-step lookahead RL planning is NP-hard for every fixed rational discount factor yet give a randomized polynomial-time approximation scheme.
The paper resolves open questions about reinforcement learning with multi-step transition lookahead. It shows exact planning remains NP-hard for every fixed rational discount factor in (0,1), not just discounts arbitrarily close to one, and introduces a randomized polynomial-time approximation scheme for every fixed lookahead depth. Extending to unknown transitions and stochastic rewards via optimism and variance-adaptive confidence bounds, the algorithm achieves cumulative regret matching classical tabular discounted RL up to logarithmic factors.