Prediction with Corrupted Expert Advice

TL;DR

This paper studies prediction with expert advice in a stochastic environment with adversarial corruption, showing that a modified Multiplicative Weights algorithm achieves optimal constant regret regardless of corruption level.

Contribution

It introduces a variant of the Multiplicative Weights algorithm that guarantees constant regret under corrupted stochastic feedback, and compares the performance of FTRL and OMD in this setting.

Findings

Modified Multiplicative Weights achieves constant regret.

FTRL outperforms OMD in corrupted stochastic environments.

Algorithm performs optimally across various corruption levels.

Abstract

We revisit the fundamental problem of prediction with expert advice, in a setting where the environment is benign and generates losses stochastically, but the feedback observed by the learner is subject to a moderate adversarial corruption. We prove that a variant of the classical Multiplicative Weights algorithm with decreasing step sizes achieves constant regret in this setting and performs optimally in a wide range of environments, regardless of the magnitude of the injected corruption. Our results reveal a surprising disparity between the often comparable Follow the Regularized Leader (FTRL) and Online Mirror Descent (OMD) frameworks: we show that for experts in the corrupted stochastic regime, the regret performance of OMD is in fact strictly inferior to that of FTRL.