Reinforcement learning plans near-optimally despite hard multi-step lookahead
Near-Optimal Reinforcement Learning with Multi-Step Transition Lookahead
Machine Learning
Summary
Deciding the best actions in a smart system that can see multiple future steps can be very difficult to solve exactly. The authors show that finding the perfect solution remains hard even when the system values the future less strongly. However, they also provide a way to find near-perfect solutions efficiently for any fixed lookahead depth. They extend this approach to learning when the environment is unknown, achieving performance close to the best possible. This means that even if exact planning is very complex, practical near-optimal planning and learning can be done efficiently.
What this means in practice
- •For robotics engineers: Design robots that efficiently plan actions with foresight of multi-step outcomes despite problem complexity.
- •For automated control teams: Create control systems that learn near-optimal policies quickly even with complex multi-step future state evaluations.
Authors
Corentin Pla, Hugo Richard, Marc Abeille, Vianney Perchet
Abstract
We study reinforcement learning (RL) with transition look-ahead, where the agent may observe which states would be visited upon playing any sequence of $\ell$ actions before deciding its course of action. Although look-ahead can substantially improve achievable performance, it is known that optimal planning with multi-step transition look-ahead is NP-hard, but this hardness was established using discount factors arbitrarily close to one. It was therefore unknown whether the problem remains hard for any discount factor, and whether near-optimal planning can nevertheless be performed efficiently. We resolve both questions. First, we show that for every fixed rational discount factor ($γ\in(0,1)$), exact planning remains NP-hard. Second, we introduce a randomized polynomial-time approximation scheme for every fixed look-ahead depth. We then extend our approach to unknown transitions and stochastic rewards using optimism and variance-adaptive confidence bounds. The resulting algorithm achieves cumulative regret whose leading term matches classical tabular discounted RL up to logarithmic factors. Thus, although exact planning with transition look-ahead is NP-hard, efficient near-optimal planning and learning remain possible.