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Main Authors: Liu, Meitong, Zhang, Xiaoyuan, Xie, Chulin, Donahue, Kate, Zhao, Han
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.21764
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author Liu, Meitong
Zhang, Xiaoyuan
Xie, Chulin
Donahue, Kate
Zhao, Han
author_facet Liu, Meitong
Zhang, Xiaoyuan
Xie, Chulin
Donahue, Kate
Zhao, Han
contents Multi-objective learning (MOL) aims to learn under multiple potentially conflicting objectives and strike a proper balance. While recent preference-guided MOL methods often rely on additional optimization objectives or constraints, we consider the classic Tchebycheff scalarization (TCH) that naturally allows for locating solutions with user-specified trade-offs. Due to its minimax formulation, directly optimizing TCH often leads to training oscillation and stagnation. In light of this limitation, we propose an adaptive online mirror descent algorithm for TCH, called (Ada)OMD-TCH. One of our main ingredients is an adaptive online-to-batch conversion that significantly improves solution optimality over traditional conversion in practice while maintaining the same theoretical convergence guarantees. We show that (Ada)OMD-TCH achieves a convergence rate of $\mathcal O(\sqrt{\log m/T})$, where $m$ is the number of objectives and $T$ is the number of rounds, providing a tighter dependency on $m$ in the offline setting compared to existing work. Empirically, we demonstrate on both synthetic problems and federated learning tasks that (Ada)OMD-TCH effectively smooths the training process and yields preference-guided, specific, diverse, and fair solutions.
format Preprint
id arxiv_https___arxiv_org_abs_2410_21764
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publishDate 2024
record_format arxiv
spellingShingle Adaptive Online Mirror Descent for Tchebycheff Scalarization in Multi-Objective Learning
Liu, Meitong
Zhang, Xiaoyuan
Xie, Chulin
Donahue, Kate
Zhao, Han
Machine Learning
Artificial Intelligence
Multi-objective learning (MOL) aims to learn under multiple potentially conflicting objectives and strike a proper balance. While recent preference-guided MOL methods often rely on additional optimization objectives or constraints, we consider the classic Tchebycheff scalarization (TCH) that naturally allows for locating solutions with user-specified trade-offs. Due to its minimax formulation, directly optimizing TCH often leads to training oscillation and stagnation. In light of this limitation, we propose an adaptive online mirror descent algorithm for TCH, called (Ada)OMD-TCH. One of our main ingredients is an adaptive online-to-batch conversion that significantly improves solution optimality over traditional conversion in practice while maintaining the same theoretical convergence guarantees. We show that (Ada)OMD-TCH achieves a convergence rate of $\mathcal O(\sqrt{\log m/T})$, where $m$ is the number of objectives and $T$ is the number of rounds, providing a tighter dependency on $m$ in the offline setting compared to existing work. Empirically, we demonstrate on both synthetic problems and federated learning tasks that (Ada)OMD-TCH effectively smooths the training process and yields preference-guided, specific, diverse, and fair solutions.
title Adaptive Online Mirror Descent for Tchebycheff Scalarization in Multi-Objective Learning
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2410.21764