The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning

Optimization of conflicting functions is paramount importance in decision making, and real world applications frequently involve data that uncertain or unknown, resulting multi-objective optimization (MOO) problems stochastic type. We study the multi-gradient (SMG) method, seen as an extension classical gradient method for single-objective optimization. At each iteration SMG a direction calculated by solving quadratic subproblem, it shown this biased even when all individual estimators are unbiased. establish rates to compute point Pareto front, order similar what known both convex strongly cases. The analysis handles bias unknown priori weights limiting point. framed into Pareto-front type algorithm calculating approximation entire front. capable robustly determining fronts number synthetic test problems. One can apply any MOO problem arising from supervised machine learning, we report results logistic binary classification where multiple objectives correspond distinct-sources groups.