# Fast Rates for Bandit Optimization with Upper-Confidence Frank-Wolfe

## TL;DR

This paper introduces the Upper-Confidence Frank-Wolfe algorithm for bandit optimization, providing theoretical guarantees for minimizing a global loss function in a broad class of problems with applications across statistics and machine learning.

## Contribution

It presents a novel algorithm combining bandit techniques with Frank-Wolfe optimization and offers theoretical performance guarantees for various function classes.

## Key findings

- The algorithm achieves fast convergence rates.
- Theoretical guarantees are established for different function classes.
- Results demonstrate near-optimal performance in bandit optimization.

## Abstract

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.