Invariant Risk Minimization Games

TL;DR

This paper introduces an invariant risk minimization framework modeled as a game among environments, providing a simple algorithm that finds invariant predictors with strong theoretical guarantees and improved empirical stability.

Contribution

It formulates invariant risk minimization as a Nash equilibrium game, offering a new, simpler training algorithm with theoretical equivalence to invariant predictors across environments.

Findings

The proposed game-theoretic approach finds invariant predictors.

The algorithm achieves similar or better accuracy with lower variance.

Nash equilibria correspond to invariant predictors even with nonlinear classifiers.

Abstract

The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many environments and finding invariant predictors reduces the effect of spurious features by concentrating models on features that have a causal relationship with the outcome. In this work, we pose such invariant risk minimization as finding the Nash equilibrium of an ensemble game among several environments. By doing so, we develop a simple training algorithm that uses best response dynamics and, in our experiments, yields similar or better empirical accuracy with much lower variance than the challenging bi-level optimization problem of Arjovsky et al. (2019). One key theoretical contribution is showing that the set of Nash equilibria for the proposed game are equivalent to the set of invariant predictors for any finite number of environments, even with nonlinear classifiers and transformations. As a result, our method also retains the generalization guarantees to a large set of environments shown in Arjovsky et al. (2019). The proposed algorithm adds to the collection of successful game-theoretic machine learning algorithms such as generative adversarial networks.