Bandit Convex Optimisation

TL;DR

This work reviews and applies various optimization tools to bandit convex optimization, highlighting their nuances and introducing some novel algorithmic applications and minor bounds improvements.

Contribution

It systematically explores existing tools in bandit convex optimization, applying them in new ways and refining some bounds, with a focus on comprehensive coverage.

Findings

Application of existing tools in novel ways

Minor improvements in bounds

Clarification of assumptions and setups

Abstract

Bandit convex optimisation is a fundamental framework for studying zeroth-order convex optimisation. This book covers the many tools used for this problem, including cutting plane methods, interior point methods, continuous exponential weights, gradient descent and online Newton step. The nuances between the many assumptions and setups are explained. Although there is not much truly new here, some existing tools are applied in novel ways to obtain new algorithms. A few bounds are improved in minor ways.