Unleashing Linear Optimizers for Group-Fair Learning and Optimization
This work addresses the problem of efficiently incorporating fairness and multi-objective considerations into machine learning and optimization for practitioners, though it is incremental as it builds on existing linear and convex optimization techniques.
The paper tackles the computational challenge of optimizing complex objectives, such as group fairness in learning, beyond average performance, and proves that optimizing arbitrary objectives over a constant number of groups is not significantly harder than average performance, with a polynomial-time reduction using linear optimizers.
Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for example, when balancing performance or loss with fairness across people. We prove that, from a computational perspective, optimizing arbitrary objectives that take into account performance over a small number of groups is not significantly harder to optimize than average performance. Our main result is a polynomial-time reduction that uses a linear optimizer to optimize an arbitrary (Lipschitz continuous) function of performance over a (constant) number of possibly-overlapping groups. This includes fairness objectives over small numbers of groups, and we further point out that other existing notions of fairness such as individual fairness can be cast as convex optimization and hence more standard convex techniques can be used. Beyond learning, our approach applies to multi-objective optimization, more generally.