Bandit Optimization with Upper-Confidence Frank-Wolfe

We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily a cumulative loss. This framework allows us to study a very general class of problems, with applications in statistics, machine learning, and other fields. To solve this problem, we introduce the Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and convex optimization. We show upper bounds on the optimization error of this algorithm over various classes of functions, and discuss the optimality of these results.