An Adaptive Projected-Gradient Algorithm for Sample-Average Approximations of Stochastic Multi-Objective Optimization

What the math gives to ML

The paper provides a function-value-free adaptive projected-gradient method for stochastic multi-objective problems, where a regularized combination of sample gradients produces a feasible common descent step and the regularization is updated from the projected step length. The transferable asset is not merely multi-task gradient balancing, which is already known, but the coupling of a simplex-constrained multi-gradient certificate with projection-based adaptivity and no line search or objective-value evaluations. A practical neural-network adaptation is a multi-task optimizer that computes one minibatch gradient per task, selects a regularized convex combination, projects the parameter update onto a trust region or parameter constraint set, and adjusts the regularization using the observed projected displacement.