Asymptotically-Optimal Gaussian Bandits with Side Observations
This work addresses a fundamental problem in multi-armed bandit theory for researchers and practitioners, providing optimal regret guarantees in a general feedback model that includes standard and graph-structured cases as special cases.
The paper tackles the problem of Gaussian bandits with general side information, where playing an arm reveals information about others via a known matrix, and presents the first asymptotically optimal algorithm for this setting, achieving a lower bound on regret derived from an LP optimization.
We study the problem of Gaussian bandits with general side information, as first introduced by Wu, Szepesvari, and Gyorgy. In this setting, the play of an arm reveals information about other arms, according to an arbitrary a priori known side information matrix: each element of this matrix encodes the fidelity of the information that the ``row'' arm reveals about the ``column'' arm. In the case of Gaussian noise, this model subsumes standard bandits, full-feedback, and graph-structured feedback as special cases. In this work, we first construct an LP-based asymptotic instance-dependent lower bound on the regret. The LP optimizes the cost (regret) required to reliably estimate the suboptimality gap of each arm. This LP lower bound motivates our main contribution: the first known asymptotically optimal algorithm for this general setting.