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Multiple-objective optimization (MOO) aims to simultaneously optimizemultiple conflicting objectives and has found important applications in machinelearning, such as minimizing classification loss and discrepancy in treatingdifferent populations for fairness. At optimality, further optimizing oneobjective will necessarily harm at least another objective, and decision-makersneed to comprehensively explore multiple optima (called Pareto front) topinpoint one final solution. We address the efficiency of finding the Paretofront. First, finding the front from scratch using stochastic multi-gradientdescent (SMGD) is expensive with large neural networks and datasets. We proposeto explore the Pareto front as a manifold from a few initial optima, based on apredictor-corrector method. Second, for each exploration step, the predictorsolves a large-scale linear system that scales quadratically in the number ofmodel parameters and requires one backpropagation to evaluate a second-orderHessian-vector product per iteration of the solver. We propose a Gauss-Newtonapproximation that only scales linearly, and that requires only first-orderinner-product per iteration. This also allows for a choice between the MINRESand conjugate gradient methods when approximately solving the linear system.The innovations make predictor-corrector possible for large networks.Experiments on multi-objective (fairness and accuracy) misinformation detectiontasks show that 1) the predictor-corrector method can find Pareto fronts betterthan or similar to SMGD with less time; and 2) the proposed first-order methoddoes not harm the quality of the Pareto front identified by the second-ordermethod, while further reduce running time.

Efficient first-order predictor-corrector multiple objective optimization for fair misinformation detection