On the Global Optima of Kernelized Adversarial Representation Learning

TL;DR

This paper provides a theoretical analysis and closed-form solutions for kernelized adversarial representation learning, demonstrating its effectiveness in achieving invariant data representations with guarantees, and comparing favorably to existing methods.

Contribution

It introduces a spectral learning approach for global optima in kernelized adversarial learning, extending analysis from linear to non-linear functions with performance guarantees.

Findings

Closed-form solutions for linear case global optima.

Performance bounds on utility and invariance.

Empirical results showing comparable utility-invariance trade-offs.

Abstract

Adversarial representation learning is a promising paradigm for obtaining data representations that are invariant to certain sensitive attributes while retaining the information necessary for predicting target attributes. Existing approaches solve this problem through iterative adversarial minimax optimization and lack theoretical guarantees. In this paper, we first study the "linear" form of this problem i.e., the setting where all the players are linear functions. We show that the resulting optimization problem is both non-convex and non-differentiable. We obtain an exact closed-form expression for its global optima through spectral learning and provide performance guarantees in terms of analytical bounds on the achievable utility and invariance. We then extend this solution and analysis to non-linear functions through kernel representation. Numerical experiments on UCI, Extended Yale B and CIFAR-100 datasets indicate that, (a) practically, our solution is ideal for "imparting" provable invariance to any biased pre-trained data representation, and (b) empirically, the trade-off between utility and invariance provided by our solution is comparable to iterative minimax optimization of existing deep neural network based approaches. Code is available at https://github.com/human-analysis/Kernel-ARL