{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/direction-oriented-multi-objective-learning","title":"Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms","arxiv_id":"2305.18409","date":"2023-05-28","proceeding":"NeurIPS 2023 11","authors":["Peiyao Xiao","Hao Ban","Kaiyi Ji"],"abstract":"Multi-objective optimization (MOO) has become an influential framework in many machine learning problems with multiple objectives such as learning with multiple criteria and multi-task learning (MTL). In this paper, we propose a new direction-oriented multi-objective problem by regularizing the common descent direction within a neighborhood of a direction that optimizes a linear combination of objectives such as the average loss in MTL. This formulation includes GD and MGDA as special cases, enjoys the direction-oriented benefit as in CAGrad, and facilitates the design of stochastic algorithms. To solve this problem, we propose Stochastic Direction-oriented Multi-objective Gradient descent (SDMGrad) with simple SGD type of updates, and its variant SDMGrad-OS with an efficient objective sampling in the setting where the number of objectives is large. For a constant-level regularization parameter $\\lambda$, we show that SDMGrad and SDMGrad-OS provably converge to a Pareto stationary point with improved complexities and milder assumptions. For an increasing $\\lambda$, this convergent point reduces to a stationary point of the linear combination of objectives. We demonstrate the superior performance of the proposed methods in a series of tasks on multi-task supervised learning and reinforcement learning. 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