{"ID":2851439,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.19158","arxiv_id":"2510.19158","title":"Instance-Dependent Regret Bounds for Nonstochastic Linear Partial Monitoring","abstract":"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.","short_abstract":"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 manne...","url_abs":"https://arxiv.org/abs/2510.19158","url_pdf":"https://arxiv.org/pdf/2510.19158v2","authors":"[\"Federico Di Gennaro\",\"Khaled Eldowa\",\"Nicolò Cesa-Bianchi\"]","published":"2025-10-22T01:28:20Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"LoRA\"]","has_code":false}