Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batching

We study reinforcement learning (RL) with transition look-ahead, where the agent may observe which states would be visited upon playing any sequence of actions before deciding its course of action. Although look-ahead can substantially improve achievable performance, [1] showed that optimal planning with multi-step transition look-ahead is NP-hard. However, this hardness was established using a discount factor close to one. It was therefore unknown whether the problem remains hard for every discount factor, and whether near-optimal planning can nevertheless be performed efficiently. We resolve both questions. First, we show that for every fixed discount factor, exact planning remains NP-hard. Second, we introduce a randomized polynomial-time approximation scheme for every fixed look-ahead depth. Third, we extend our approach to account for unknown transitions. We empirically validate the soundness of our results on the wind-farm storage-control benchmark of [2], showing that our approach, optimally accounting for -step look-ahead information, offers substantially better performance than existing algorithms. [1] Corentin Pla, Hugo Richard, Marc Abeille, Nadav Merlis, Vianney Perchet : On the Hardness of Reinforcement Learning with Transition Look-Ahead [2] Chenbei Lu, Zaiwei Chen, Tongxin Li, Chenye Wu, Adam Wierman : Reinforcement Learning with Imperfect Transition Predictions: A Bellman-Jensen Approach

Multi-step predictions of future transition realizations can improve reinforcement learning, but their value remains difficult to quantify. Directly including these predictions in the state can lead to exponential state-space growth, making direct dynamic programming computationally expensive. We study discounted finite MDPs under a block-feedback protocol: at the start of each K-period block, the decision maker observes $K$-step probabilistic transition predictions for a subset of actions and adapts decisions to observed states within the block. We show that the optimal value satisfies a Bayesian Bellman equation on the original state space. This representation reveals that predictive information creates value by recursively changing the local order of maximization and expectation in the Bellman expansion. We formalize this effect through a Bellman--Jensen analysis and quantify the effects of prediction horizon, error, action coverage, and within-block feedback. We propose block-feedback Bayesian offline learning with online adaptation (BF--BOLA), a model-based algorithm for learning near-optimal policies, and establish upper and lower sample-complexity bounds that match up to logarithmic factors in the stated regimes. The results show that predictions can reduce transition learning to uncovered rows and that learning a near-optimal policy can require fewer prediction samples than estimating the Bayesian value function.

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. While such predictive information can drastically improve the achievable performance, we show that using this information optimally comes at a potentially prohibitive computational cost. Specifically, we prove that optimal planning with one-step look-ahead ($\ell=1$) can be solved in polynomial time through a novel linear programming formulation. In contrast, for $\ell \geq 2$, the problem becomes NP-hard. Our results delineate a precise boundary between tractable and intractable cases for the problem of planning with transition look-ahead in reinforcement learning.