MAdam: Metric-Aware Multi-Objective Adam

תקציר מקורי באנגליתarXiv:2606.03904v2 Announce Type: replace Abstract: Multi-objective optimization (MOO) underlies many machine learning problems, yet MOO solvers across the loss-balancing, gradient-balancing, and Pareto-based families almost universally hand their reconciled directions to Adam~\citep{kingma2015adam}. We show this coupling introduces two systematic gaps between the solver's intent and the optimizer's execution. The first is a weighting mismatch: Adam's second-moment denominator entangles the time-varying preference vector with gradient statistics, marginalizing the preference into a history average and collapsing distinct Pareto trade-offs toward a near-uniform mixture. The second is a geometric mismatch: Adam's adaptive metric distorts the Euclidean geometry MOO solvers assume, turning ali