Parameter-Free Dynamic Regret for Unconstrained Linear Bandits

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 u_1,,u_T in 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 = _tI _t 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 O(d(1+S_T) T) up to poly-logarithmic terms without prior knowledge of S_T, thus resolving a long-standing open problem.

Reproductions