Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization

• URL: http://arxiv.org/abs/2504.02833v1
• Date: Sun, 16 Mar 2025 11:05:51 GMT
• Title: Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization
• Authors: Sangwoo Park, Stefan Vlaski, Lajos Hanzo,
• Abstract summary: We propose a smooth variant of the min-max problem based on the augmented Lagrangian.<n>The proposed algorithm scales better with the number of objectives than subgradient-based strategies.
• Score: 66.51747366239299
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In multi-objective optimization, minimizing the worst objective can be preferable to minimizing the average objective, as this ensures improved fairness across objectives. Due to the non-smooth nature of the resultant min-max optimization problem, classical subgradient-based approaches typically exhibit slow convergence. Motivated by primal-dual consensus techniques in multi-agent optimization and learning, we formulate a smooth variant of the min-max problem based on the augmented Lagrangian. The resultant Exact Pareto Optimization via Augmented Lagrangian (EPO-AL) algorithm scales better with the number of objectives than subgradient-based strategies, while exhibiting lower per-iteration complexity than recent smoothing-based counterparts. We establish that every fixed-point of the proposed algorithm is both Pareto and min-max optimal under mild assumptions and demonstrate its effectiveness in numerical simulations.

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