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Spectral Bellman Method: Unifying Representation and Exploration in RL

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Reinforcement learningrepresetation learning
Abstract:

Representation learning is critical to the empirical and theoretical success of reinforcement learning. However, many existing methods are induced from model-learning aspects, misaligning them with the RL task in hand. This work introduces the Spectral Bellman Method, a novel framework derived from the Inherent Bellman Error (IBE) condition. It aligns representation learning with the fundamental structure of Bellman updates across a space of possible value functions, making it directly suited for value-based RL. Our key insight is a fundamental spectral relationship: under the zero-IBE condition, the transformation of a distribution of value functions by the Bellman operator is intrinsically linked to the feature covariance structure. This connection yields a new, theoretically-grounded objective for learning state-action features that capture this Bellman-aligned covariance, requiring only a simple modification to existing algorithms. We demonstrate that our learned representations enable structured exploration by aligning feature covariance with Bellman dynamics, improving performance in hard-exploration and long-horizon tasks. Our framework naturally extends to multi-step Bellman operators, offering a principled path toward learning more powerful and structurally sound representations for value-based RL.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces the Spectral Bellman Method, a framework for learning state-action representations aligned with Bellman operator structure via the Inherent Bellman Error condition. It resides in the 'Spectral and Bellman-Aligned Representation Learning' leaf, which contains only three papers total. This is a relatively sparse research direction within the broader taxonomy of fifty papers, suggesting the specific approach of deriving representations from spectral relationships in Bellman dynamics remains underexplored compared to more crowded areas like curiosity-driven exploration or multi-task learning.

The taxonomy reveals neighboring leaves focused on latent variable models and contrastive learning (six papers) and representation-driven policy frameworks (two papers), indicating alternative paradigms for constructing features in value-based RL. The paper's spectral approach diverges from these by explicitly grounding representation objectives in Bellman operator properties rather than general contrastive or latent-variable principles. Nearby branches address exploration mechanisms and theoretical foundations under structural assumptions like low-rank MDPs, but the paper's focus on feature covariance aligned with value function transformations occupies a distinct conceptual niche within representation learning frameworks.

Across three contributions, the analysis examined twenty-eight candidate papers from semantic search and citation expansion. For the core Spectral Bellman Method framework, ten candidates were reviewed with zero refutations found. The theoretically-grounded objective for Bellman-aligned features examined eight candidates, also yielding no clear prior overlap. The multi-step extension reviewed ten candidates without refutation. These statistics reflect a limited search scope—not an exhaustive survey—but suggest that among the top-ranked semantically similar work, no single paper directly anticipates the spectral covariance formulation proposed here.

Given the sparse taxonomy leaf and absence of refutations among twenty-eight examined candidates, the work appears to occupy a relatively novel position within its immediate research neighborhood. However, the limited search scale means potentially relevant work outside the top semantic matches may exist. The analysis captures the paper's distinctiveness within spectral and Bellman-aligned methods but cannot rule out incremental overlap with broader representation learning literature not surfaced by this search.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
28
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: representation learning and exploration in value-based reinforcement learning. The field organizes around several major branches that address complementary challenges in learning effective policies. Representation Learning Frameworks and Objectives focuses on how agents construct compact, informative state encodings—ranging from spectral methods that align representations with value structure to approaches leveraging latent variables or prototypical embeddings. Exploration Strategies and Mechanisms examines how agents gather informative experience, including count-based methods like Count-Based Exploration[9], curiosity-driven schemes such as Curiosity Contrastive[41], and structured approaches that exploit model uncertainty or intrinsic rewards. Theoretical Foundations and Structural Assumptions investigates formal guarantees under settings like low-rank MDPs (Low-Rank MDPs[1]) or block structures, while Empirical Methods and Algorithms emphasizes practical techniques for deep RL, multitask learning (Offline Multitask[4]), and hierarchical decomposition. Application-Specific Methods tailors these ideas to domains such as navigation, robotics, and safety-critical systems. A particularly active line of work centers on aligning learned representations with the Bellman operator to ensure value functions remain tractable and sample-efficient. The Spectral Bellman Method[0] exemplifies this direction by using spectral decompositions to capture value structure, positioning itself alongside efforts like SVD Exploration[6] and Laplacian Options[44] that exploit eigenstructure for both representation and exploration. In contrast, Representation-Driven RL[3] and Exploration for Generalization[5] emphasize how representation quality directly shapes exploration efficiency and generalization across tasks. These contrasting emphases—whether to prioritize Bellman-aligned encodings or broader exploratory objectives—reflect an ongoing tension between theoretical elegance and empirical flexibility. The Spectral Bellman Method[0] sits squarely within the spectral and Bellman-aligned cluster, sharing conceptual ground with works that decompose transition or value operators, yet it distinguishes itself by tightly coupling spectral analysis with value-based learning guarantees.

Claimed Contributions

Spectral Bellman Method framework for representation learning

The authors propose a new framework that learns state-action features by exploiting a spectral relationship between the Bellman operator and feature covariance structure under the zero-IBE condition. This approach aligns representation learning with Bellman dynamics, making it directly suited for value-based RL.

10 retrieved papers
Theoretically-grounded objective for learning Bellman-aligned features

The authors derive a novel objective function (SBM Loss) based on the spectral properties of the Bellman operator that learns features whose covariance captures Bellman-aligned structure. This objective overcomes the limitations of direct Bellman error minimization and can be integrated into existing RL algorithms with minimal changes.

8 retrieved papers
Extension to multi-step Bellman operators

The authors show that their spectral representation learning approach can be extended to handle multi-step Bellman operators such as Retrace, providing a principled method for learning representations that work with more powerful temporal difference targets.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Spectral Bellman Method framework for representation learning

The authors propose a new framework that learns state-action features by exploiting a spectral relationship between the Bellman operator and feature covariance structure under the zero-IBE condition. This approach aligns representation learning with Bellman dynamics, making it directly suited for value-based RL.

Contribution

Theoretically-grounded objective for learning Bellman-aligned features

The authors derive a novel objective function (SBM Loss) based on the spectral properties of the Bellman operator that learns features whose covariance captures Bellman-aligned structure. This objective overcomes the limitations of direct Bellman error minimization and can be integrated into existing RL algorithms with minimal changes.

Contribution

Extension to multi-step Bellman operators

The authors show that their spectral representation learning approach can be extended to handle multi-step Bellman operators such as Retrace, providing a principled method for learning representations that work with more powerful temporal difference targets.

Table of Contents