A Second-Order Method for Stochastic Bandit Convex Optimisation

TL;DR

This paper presents a new second-order method for stochastic bandit convex optimization that achieves near-optimal regret bounds, improving efficiency in high-dimensional settings with unknown minimizer location.

Contribution

The paper introduces a simple, efficient second-order algorithm for zeroth-order stochastic convex bandits with provably tight regret bounds.

Findings

Regret bound of $(1 + r/d)[d^{1.5} \sqrt{n} + d^3]$ proven for the algorithm

Algorithm performs well in high-dimensional stochastic convex bandit problems

Regret scales favorably with dimension and horizon

Abstract

We introduce a simple and efficient algorithm for unconstrained zeroth-order stochastic convex bandits and prove its regret is at most $(1 + r/d)[d^{1.5} \sqrt{n} + d^3] polylog(n, d, r)$ where $n$ is the horizon, $d$ the dimension and $r$ is the radius of a known ball containing the minimiser of the loss.