Parameter-Free Dynamic Regret for Unconstrained Linear Bandits

• URL: http://arxiv.org/abs/2603.25916v1
• Date: Thu, 26 Mar 2026 21:16:18 GMT
• Title: Parameter-Free Dynamic Regret for Unconstrained Linear Bandits
• Abstract summary: We study dynamic regret in unconstrained adversarial linear bandit problems.<n>We provide the first algorithm for linear bandits achieving the optimal regret guarantee of order.
• Score: 21.35587581980097
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study dynamic regret minimization in unconstrained adversarial linear bandit problems. In this setting, a learner must minimize the cumulative loss relative to an arbitrary sequence of comparators $\boldsymbol{u}_1,\ldots,\boldsymbol{u}_T$ in $\mathbb{R}^d$, but receives only point-evaluation feedback on each round. We provide a simple approach to combining the guarantees of several bandit algorithms, allowing us to optimally adapt to the number of switches $S_T = \sum_t\mathbb{I}\{\boldsymbol{u}_t \neq \boldsymbol{u}_{t-1}\}$ of an arbitrary comparator sequence. In particular, we provide the first algorithm for linear bandits achieving the optimal regret guarantee of order $\mathcal{O}\big(\sqrt{d(1+S_T) T}\big)$ up to poly-logarithmic terms without prior knowledge of $S_T$, thus resolving a long-standing open problem.

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