Adversaries in Online Learning Revisited: with applications in Robust Optimization and Adversarial training

TL;DR

This paper clarifies the concept of adversaries in online learning, distinguishes between anticipative and non-anticipative adversaries, and applies this understanding to develop a general approach for robust optimization and adversarial training using a game-theoretic framework.

Contribution

It introduces a rigorous distinction between types of adversaries in online learning and develops a meta-game approach for robust optimization and adversarial training.

Findings

Different types of adversaries affect regret guarantees.

The proposed meta-game approach effectively solves robust optimization problems.

The method generalizes previous approaches like arXiv:1402.6361.

Abstract

We revisit the concept of "adversary" in online learning, motivated by solving robust optimization and adversarial training using online learning methods. While one of the classical setups in online learning deals with the "adversarial" setup, it appears that this concept is used less rigorously, causing confusion in applying results and insights from online learning. Specifically, there are two fundamentally different types of adversaries, depending on whether the "adversary" is able to anticipate the exogenous randomness of the online learning algorithms. This is particularly relevant to robust optimization and adversarial training because the adversarial sequences are often anticipative, and many online learning algorithms do not achieve diminishing regret in such a case. We then apply this to solving robust optimization problems or (equivalently) adversarial training problems via online learning and establish a general approach for a large variety of problem classes using imaginary play. Here two players play against each other, the primal player playing the decisions and the dual player playing realizations of uncertain data. When the game terminates, the primal player has obtained an approximately robust solution. This meta-game allows for solving a large variety of robust optimization and multi-objective optimization problems and generalizes the approach of arXiv:1402.6361.