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

On the Global Optima of Kernelized Adversarial Representation Learning