{"ID":3004680,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-05T11:43:53.432517148Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.03904","arxiv_id":"2606.03904","title":"MAdam: Metric-Aware Multi-Objective Adam","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~\\cite{kingma2015adam}. We show this coupling introduces two systematic gaps between the solver's intent and the optimizer's execution. The first is a \\emph{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 \\emph{geometric mismatch}: Adam's adaptive metric distorts the Euclidean geometry MOO solvers assume, turning aligned objectives into apparent conflicts. To resolve both jointly, we introduce \\textbf{MAdam} (Metric-Aware Multi-Objective Adam), a drop-in wrapper that leaves both solver and optimizer unchanged. MAdam preconditions the reconciled direction by the preference-conditioned curvature of the scalarized objective; on this whitened input, Adam's second moment collapses to identity, so the realized update is governed by the preference-conditioned metric. Across multi-task learning, Pareto-front recovery, physics-informed neural networks, and medical imaging, MAdam consistently improves over Adam for every solver family.","short_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~\\cite{kingma2015adam}. We show this coupling introduces two systematic gaps between the solver...","url_abs":"https://arxiv.org/abs/2606.03904","url_pdf":"https://arxiv.org/pdf/2606.03904v1","authors":"[\"Fengbei Liu\",\"Rachit Saluja\",\"Sunwoo Kwak\",\"Ruibo Wang\",\"Ruining Deng\",\"Heejong Kim\",\"Johannes C. Paetzold\",\"Mert R. Sabuncu\"]","published":"2026-06-02T17:00:15Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CV\"]","methods":"[]","has_code":false}