Information-Theoretic Generalization Bounds for Sequential Decision Making
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911675406352384 |
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| author | Futami, Futoshi Fujisawa, Masahiro |
| author_facet | Futami, Futoshi Fujisawa, Masahiro |
| contents | Information-theoretic generalization bounds based on the supersample construction are a central tool for algorithm-dependent generalization analysis in the batch i.i.d.~setting. However, existing supersample conditional mutual information (CMI) bounds do not directly apply to sequential decision-making problems such as online learning, streaming active learning, and bandits, where data are revealed adaptively and the learner evolves along a causal trajectory. To address this limitation, we develop a sequential supersample framework that separates the learner filtration from a proof-side enlargement used for ghost-coordinate comparisons. Under a row-wise exchangeability assumption, the sequential generalization gap is controlled by sequential CMI, a sum of roundwise selector--loss information terms. We also establish a Bernstein-type refinement that yields faster rates under suitable variance conditions. The selector-SCMI proof strategy applies to online learning, streaming active learning with importance weighting, and stochastic multi-armed bandits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12190 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information-Theoretic Generalization Bounds for Sequential Decision Making Futami, Futoshi Fujisawa, Masahiro Machine Learning Information-theoretic generalization bounds based on the supersample construction are a central tool for algorithm-dependent generalization analysis in the batch i.i.d.~setting. However, existing supersample conditional mutual information (CMI) bounds do not directly apply to sequential decision-making problems such as online learning, streaming active learning, and bandits, where data are revealed adaptively and the learner evolves along a causal trajectory. To address this limitation, we develop a sequential supersample framework that separates the learner filtration from a proof-side enlargement used for ghost-coordinate comparisons. Under a row-wise exchangeability assumption, the sequential generalization gap is controlled by sequential CMI, a sum of roundwise selector--loss information terms. We also establish a Bernstein-type refinement that yields faster rates under suitable variance conditions. The selector-SCMI proof strategy applies to online learning, streaming active learning with importance weighting, and stochastic multi-armed bandits. |
| title | Information-Theoretic Generalization Bounds for Sequential Decision Making |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.12190 |