Derivative-Free & Order-Robust Optimisation

TL;DR

This paper introduces Vroom, a zero'th order optimization algorithm designed for non-stationary and adversarial environments, achieving vanishing regret and addressing a rarely explored aspect of simple regret in online learning.

Contribution

It formalizes order-robust optimization as online learning and presents Vroom, the first algorithm targeting simple regret in adversarial settings with proven performance.

Findings

Vroom achieves vanishing regret in non-stationary environments.

It recovers favorable rates under stochastic reward processes.

Addresses a novel challenge in simple regret for adversarial scenarios.

Abstract

In this paper, we formalise order-robust optimisation as an instance of online learning minimising simple regret, and propose Vroom, a zero'th order optimisation algorithm capable of achieving vanishing regret in non-stationary environments, while recovering favorable rates under stochastic reward-generating processes. Our results are the first to target simple regret definitions in adversarial scenarios unveiling a challenge that has been rarely considered in prior work.