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Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batching

Nadav Merlis

TL;DR

The paper addresses planning and learning in episodic, tabular MDPs with multi-step lookahead information observed before acting. It introduces adaptive batching policies (ABPs) that allow state-dependent batching horizons and derives their optimal Bellman equations, enabling tractable planning via an augmented batched MDP. An AL-UCB algorithm delivers optimistic learning with near-optimal regret, showing ABPs can outperform fixed batching and MPC strategies, with regret bounds that scale polylogarithmically in the horizon and horizon-dependent factors in $\ell$. The results provide a principled framework for exploiting multi-step lookahead in reinforcement learning and motivate future work on tractable approximations and extensions to imperfect predictions and deep RL.

Abstract

We study tabular reinforcement learning problems with multiple steps of lookahead information. Before acting, the learner observes $\ell$ steps of future transition and reward realizations: the exact state the agent would reach and the rewards it would collect under any possible course of action. While it has been shown that such information can drastically boost the value, finding the optimal policy is NP-hard, and it is common to apply one of two tractable heuristics: processing the lookahead in chunks of predefined sizes ('fixed batching policies'), and model predictive control. We first illustrate the problems with these two approaches and propose utilizing the lookahead in adaptive (state-dependent) batches; we refer to such policies as adaptive batching policies (ABPs). We derive the optimal Bellman equations for these strategies and design an optimistic regret-minimizing algorithm that enables learning the optimal ABP when interacting with unknown environments. Our regret bounds are order-optimal up to a potential factor of the lookahead horizon $\ell$, which can usually be considered a small constant.

Reinforcement Learning with Multi-Step Lookahead Information Via Adaptive Batching

TL;DR

The paper addresses planning and learning in episodic, tabular MDPs with multi-step lookahead information observed before acting. It introduces adaptive batching policies (ABPs) that allow state-dependent batching horizons and derives their optimal Bellman equations, enabling tractable planning via an augmented batched MDP. An AL-UCB algorithm delivers optimistic learning with near-optimal regret, showing ABPs can outperform fixed batching and MPC strategies, with regret bounds that scale polylogarithmically in the horizon and horizon-dependent factors in . The results provide a principled framework for exploiting multi-step lookahead in reinforcement learning and motivate future work on tractable approximations and extensions to imperfect predictions and deep RL.

Abstract

We study tabular reinforcement learning problems with multiple steps of lookahead information. Before acting, the learner observes steps of future transition and reward realizations: the exact state the agent would reach and the rewards it would collect under any possible course of action. While it has been shown that such information can drastically boost the value, finding the optimal policy is NP-hard, and it is common to apply one of two tractable heuristics: processing the lookahead in chunks of predefined sizes ('fixed batching policies'), and model predictive control. We first illustrate the problems with these two approaches and propose utilizing the lookahead in adaptive (state-dependent) batches; we refer to such policies as adaptive batching policies (ABPs). We derive the optimal Bellman equations for these strategies and design an optimistic regret-minimizing algorithm that enables learning the optimal ABP when interacting with unknown environments. Our regret bounds are order-optimal up to a potential factor of the lookahead horizon , which can usually be considered a small constant.
Paper Structure (36 sections, 20 theorems, 119 equations, 1 figure, 4 algorithms)

This paper contains 36 sections, 20 theorems, 119 equations, 1 figure, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Setting
  4. Lookahead information.
  5. Lookahead Policies
  6. Adaptive batching policies (ABPs)
  7. Values and performance criterion.
  8. Optimal Planning
  9. Efficient Value Computation.
  10. Learning the Optimal ABP
  11. Comparison to one-step lookahead.
  12. Tightness for $\ell>1$.
  13. Conclusions and Future Work
  14. Data Generation Process
  15. Lookahead Sampling Procedure.
  16. ...and 21 more sections

Key Result

Proposition 4.0

There exists an optimal adaptive batching policy $\pi^{*}$ that maximizes the value $V^{\pi}_1(s)$ simultaneously for all $s\in\mathcal{S}$. For any $h\in[H]$ and $s\in\mathcal{S}$, the optimal values are given by the dynamic programming equation where $V^{*}_{H+1}(s) = 0$ for all $s\in\mathcal{S}$ and the expectation samples fresh lookahead information independently between timesteps. Moreover,

Figures (1)

  • Figure : Extended Adaptive Batching Policies

Theorems & Definitions (41)

  • Example 1
  • Claim 3.0
  • Claim 3.1: informal
  • Remark 1
  • Proposition 4.0
  • Theorem 5.0
  • Remark 2
  • Lemma 1
  • proof
  • Corollary 2
  • ...and 31 more