Fast Rates for Bandit Optimization with Upper-Confidence Frank-Wolfe
This work addresses a general class of optimization problems with bandit feedback, applicable in statistics and machine learning, but appears incremental as it builds on existing techniques.
The paper tackles the problem of bandit optimization by proposing the Upper-Confidence Frank-Wolfe algorithm, which achieves theoretical guarantees for minimizing a global loss function across various function classes, with results discussed in terms of optimality.
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 analyze the Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and convex optimization. We give theoretical guarantees for the performance of this algorithm over various classes of functions, and discuss the optimality of these results.