Near-Optimal Reinforcement Learning with Multi-Step Transition Lookahead

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 ($\gamma\in(0,1)$), 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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.11807 [stat.ML]

(or arXiv:2609.11807v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.11807 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.