Highly-Smooth Zero-th Order Online Optimization Vianney Perchet

Highly-Smooth Zero-th Order Online Optimization

The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information, that is noisy function evaluations at any desired point. We focus on problems with high degrees of smoothness, such as logistic regression. We show that as oppo...

Online Learning and Blackwell Approachability with Partial Monitoring: Optimal Convergence Rates

Blackwell approachability is an online learning setup generalizing the classical problem of regret minimization by allowing for instance multi-criteria optimization, global (online) optimization of a convex loss, or online linear optimization under some cumulative constraint. We consider partial monitoring where the decision maker does not necessarily observe the outcomes of his decision (unlik...

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. T...

Fast Rates for 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. T...

Anytime optimal algorithms in stochastic multi-armed bandits - Supplementary Material