What Fundamental Structure in Reward Functions Enables Efficient Sparse-Reward Learning?

• URL: http://arxiv.org/abs/2509.03790v2
• Date: Tue, 09 Sep 2025 02:53:54 GMT
• Title: What Fundamental Structure in Reward Functions Enables Efficient Sparse-Reward Learning?
• Abstract summary: Policy-Aware Matrix Completion (PAMC) is a first concrete step toward a structural reward learning framework.<n>Our results highlight PAMC as a practical and principled tool when structural rewards exist, and as a concrete first instantiation of a broader structural reward learning perspective.
• Score: 6.908972852063454
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sparse-reward reinforcement learning (RL) remains fundamentally hard: without structure, any agent needs $\Omega(|\mathcal{S}||\mathcal{A}|/p)$ samples to recover rewards. We introduce Policy-Aware Matrix Completion (PAMC) as a first concrete step toward a structural reward learning framework. Our key idea is to exploit approximate low-rank + sparse structure in the reward matrix, under policy-biased (MNAR) sampling. We prove recovery guarantees with inverse-propensity weighting, and establish a visitation-weighted error-to-regret bound linking completion error to control performance. Importantly, when assumptions weaken, PAMC degrades gracefully: confidence intervals widen and the algorithm abstains, ensuring safe fallback to exploration. Empirically, PAMC improves sample efficiency across Atari-26 (10M steps), DM Control, MetaWorld MT50, D4RL offline RL, and preference-based RL benchmarks, outperforming DrQ-v2, DreamerV3, Agent57, T-REX/D-REX, and PrefPPO under compute-normalized comparisons. Our results highlight PAMC as a practical and principled tool when structural rewards exist, and as a concrete first instantiation of a broader structural reward learning perspective.

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