Instance-Dependent Regret Bounds for Nonstochastic Linear Partial Monitoring
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918288718561280 |
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| author | Di Gennaro, Federico Eldowa, Khaled Cesa-Bianchi, Nicolò |
| author_facet | Di Gennaro, Federico Eldowa, Khaled Cesa-Bianchi, Nicolò |
| contents | In contrast to the classic formulation of partial monitoring, linear partial monitoring can model infinite outcome spaces, while imposing a linear structure on both the losses and the observations. This setting can be viewed as a generalization of linear bandits where loss and feedback are decoupled in a flexible manner. In this work, we address a nonstochastic (adversarial), finite-actions version of the problem through a simple instance of the exploration-by-optimization method that is amenable to efficient implementation. We derive regret bounds that depend on the game structure in a more transparent manner than previous theoretical guarantees for this paradigm. Our bounds feature instance-specific quantities that reflect the degree of alignment between observations and losses, and resemble known guarantees in the stochastic setting. Notably, they achieve the standard $\sqrt{T}$ rate in easy (locally observable) games and $T^{2/3}$ in hard (globally observable) games, where $T$ is the time horizon. We instantiate these bounds in a selection of old and new partial information settings subsumed by this model, and illustrate that the achieved dependence on the game structure can be tight in interesting cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_19158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instance-Dependent Regret Bounds for Nonstochastic Linear Partial Monitoring Di Gennaro, Federico Eldowa, Khaled Cesa-Bianchi, Nicolò Machine Learning In contrast to the classic formulation of partial monitoring, linear partial monitoring can model infinite outcome spaces, while imposing a linear structure on both the losses and the observations. This setting can be viewed as a generalization of linear bandits where loss and feedback are decoupled in a flexible manner. In this work, we address a nonstochastic (adversarial), finite-actions version of the problem through a simple instance of the exploration-by-optimization method that is amenable to efficient implementation. We derive regret bounds that depend on the game structure in a more transparent manner than previous theoretical guarantees for this paradigm. Our bounds feature instance-specific quantities that reflect the degree of alignment between observations and losses, and resemble known guarantees in the stochastic setting. Notably, they achieve the standard $\sqrt{T}$ rate in easy (locally observable) games and $T^{2/3}$ in hard (globally observable) games, where $T$ is the time horizon. We instantiate these bounds in a selection of old and new partial information settings subsumed by this model, and illustrate that the achieved dependence on the game structure can be tight in interesting cases. |
| title | Instance-Dependent Regret Bounds for Nonstochastic Linear Partial Monitoring |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.19158 |