mlsanityData to 14 Oct 2026

Theoretical Barriers in Bellman-Based Reinforcement Learning

arXiv 2502.11968 ↗First posted 17 Feb 2025cs.LG cs.AIcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

Reinforcement Learning algorithms designed for high-dimensional spaces often enforce the Bellman equation on a sampled subset of states, relying on generalization to propagate knowledge across the state space. In this paper, we identify and formalize a fundamental limitation of this common approach. Specifically, we construct counterexample problems with a simple structure that this approach fails to exploit. Our findings reveal that such algorithms can neglect critical information about the problems, leading to inefficiencies. Furthermore, we extend this negative result to another approach from the literature: Hindsight Experience Replay learning state-to-state reachability.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 5 of its 16 references that are in the map. First posted on arXiv 17 Feb 2025.

Builds on

5 of 16 references.

References · 5

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2013Playing Atari with Deep Reinforcement Learningcited by 3,274
  3. 2017Hindsight Experience Replaycited by 1,136
  4. 2024Learning Formal Mathematics From Intrinsic Motivationcited by 45
  5. 2021Proving Theorems using Incremental Learning and Hindsight Experience Replaycited by 13

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  2. 2026Generalised Bellman recurrence and three dualities in sequential decision-making
  3. 2025Local-Global Learning of Interpretable Control Policies: The Interface between MPC and Reinforcement Learning
  4. 2025Spectral Bellman Method: Unifying Representation and Exploration in RL
  5. 2024Deterministic Exploration via Stationary Bellman Error Maximization
  6. 2024Taming "data-hungry" reinforcement learning? Stability in continuous state-action spaces
  7. 2025Offline Reinforcement Learning in Large State Spaces: Algorithms and Guarantees
  8. 2025Model-Based Reinforcement Learning Under Confounding