From Relative Entropy to Minimax: A Unified Framework for Coverage in MDPs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911382367109120 |
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| author | Gu, Xihe Mitra, Urbashi Javidi, Tara |
| author_facet | Gu, Xihe Mitra, Urbashi Javidi, Tara |
| contents | Targeted and deliberate exploration of state--action pairs is essential in reward-free Markov Decision Problems (MDPs). More precisely, different state-action pairs exhibit different degree of importance or difficulty which must be actively and explicitly built into a controlled exploration strategy. To this end, we propose a weighted and parameterized family of concave coverage objectives, denoted by $U_ρ$, defined directly over state--action occupancy measures. This family unifies several widely studied objectives within a single framework, including divergence-based marginal matching, weighted average coverage, and worst-case (minimax) coverage. While the concavity of $U_ρ$ captures the diminishing return associated with over-exploration, the simple closed form of the gradient of $U_ρ$ enables an explicit control to prioritize under-explored state--action pairs. Leveraging this structure, we develop a gradient-based algorithm that actively steers the induced occupancy toward a desired coverage pattern. Moreover, we show that as $ρ$ increases, the resulting exploration strategy increasingly emphasizes the least-explored state--action pairs, recovering worst-case coverage behavior in the limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11890 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Relative Entropy to Minimax: A Unified Framework for Coverage in MDPs Gu, Xihe Mitra, Urbashi Javidi, Tara Machine Learning Targeted and deliberate exploration of state--action pairs is essential in reward-free Markov Decision Problems (MDPs). More precisely, different state-action pairs exhibit different degree of importance or difficulty which must be actively and explicitly built into a controlled exploration strategy. To this end, we propose a weighted and parameterized family of concave coverage objectives, denoted by $U_ρ$, defined directly over state--action occupancy measures. This family unifies several widely studied objectives within a single framework, including divergence-based marginal matching, weighted average coverage, and worst-case (minimax) coverage. While the concavity of $U_ρ$ captures the diminishing return associated with over-exploration, the simple closed form of the gradient of $U_ρ$ enables an explicit control to prioritize under-explored state--action pairs. Leveraging this structure, we develop a gradient-based algorithm that actively steers the induced occupancy toward a desired coverage pattern. Moreover, we show that as $ρ$ increases, the resulting exploration strategy increasingly emphasizes the least-explored state--action pairs, recovering worst-case coverage behavior in the limit. |
| title | From Relative Entropy to Minimax: A Unified Framework for Coverage in MDPs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.11890 |