发表机构
Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对仅能获取样本梯度信息的随机多目标优化样本平均近似问题，提出无行搜索无函数值的自适应投影梯度算法，经多类实验验证了其实用性能。
AI 中文摘要
我们研究非空闭凸集上的随机多目标优化问题，其中每个目标为期望函数，仅能获取样本梯度信息。我们针对样本平均近似（SAA）问题，提出一种无行搜索、无函数值的自适应投影梯度算法。每次迭代计算可行的正则化多梯度步，并根据投影步长更新正则化参数。基于法锥的证书可得到SAA问题帕累托平稳性残差的下降估计和显式复杂度界；SAA梯度的一致性将SAA残差的消失特性传递至总体问题的帕累托平稳性，额外的集中论证则给出紧集上的有限样本残差界。在合成问题、分类、投资组合选择、多任务学习及机器人控制上的实验，验证了该算法的实用性能。
英文摘要
We consider stochastic multi-objective optimization over a nonempty closed convex set, where every objective is an expectation and only sample-gradient information is available. We develop a line-search-free and function-value-free adaptive projected-gradient algorithm for the sample-average approximation (SAA) problem. Each iteration computes a feasible regularized multi-gradient step and updates the regularization parameter from the projected step length. A normal-cone-based certificate yields descent estimates and an explicit complexity bound for the Pareto-stationarity residual of the SAA problem. The consistency of SAA gradients then transfers vanishing SAA residuals to Pareto stationarity for the population problem, while an additional concentration argument gives a finite-sample residual bound on compact sets. Experiments on synthetic problems, classification, portfolio selection, multi-task learning, and robot control illustrate the practical performance of our algorithm.
Comments27 pages, 6 figures
