提出新算法提升多目标优化的公平性与效率
Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization
- 基于增广拉格朗日构造平滑的极小极大优化方法
- 固定点同时满足帕累托最优和极小极大最优
- 适合大规模多目标优化，收敛更快
在多目标优化中，最小化最差目标比平均目标更利于保障各目标间的公平性。由于极小极大问题的非光滑性，传统次梯度方法通常收敛缓慢。受多智能体优化中对偶共识思想启发，本文基于增广拉格朗日构建了平滑版极小极大问题，提出精确帕累托优化算法EPO-AL。该算法在目标数增加时表现更优，且每轮计算复杂度低于近期平滑方法。在温和假设下，证明了其所有不动点均为帕累托最优与极小极大最优，并在数值实验中验证了有效性。
原文摘要 · Abstract (English)
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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