Smoothness-Adaptive Contextual Bandits

We study a non-parametric multi-armed bandit problem with stochastic covariates, where key complexity driver is the smoothness of payoff functions respect to covariates. Previous studies have focused on deriving minimax-optimal algorithms in cases it priori known how smooth are. In practice, however, typically not advance, and misspecification may severely deteriorate performance existing methods. this work, we consider framework known, when adapt unknown smoothness. First, establish that designing is, general, impossible. However, under self-similarity condition (which does reduce minimax dynamic optimization at hand), adapting possible, further devise general policy for achieving smoothness-adaptive performance. Our infers payoffs throughout decision-making process, while leveraging structure off-the-shelf non-adaptive policies. settings either differentiable or non-differentiable functions, matches (up logarithmic scale) regret rate achievable priori.