A First-Order Multi-Gradient Algorithm for Multi-Objective Bi-Level Optimization

• URL: http://arxiv.org/abs/2401.09257v2
• Date: Wed, 10 Jul 2024 08:21:47 GMT
• Title: A First-Order Multi-Gradient Algorithm for Multi-Objective Bi-Level Optimization
• Authors: Feiyang Ye, Baijiong Lin, Xiaofeng Cao, Yu Zhang, Ivor Tsang,
• Abstract summary: We study the Multi-Objective Bi-Level Optimization (MOBLO) problem. Existing gradient-based MOBLO algorithms need to compute the Hessian matrix. We propose an efficient first-order multi-gradient method for MOBLO, called FORUM.
• Score: 7.097069899573992
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the Multi-Objective Bi-Level Optimization (MOBLO) problem, where the upper-level subproblem is a multi-objective optimization problem and the lower-level subproblem is for scalar optimization. Existing gradient-based MOBLO algorithms need to compute the Hessian matrix, causing the computational inefficient problem. To address this, we propose an efficient first-order multi-gradient method for MOBLO, called FORUM. Specifically, we reformulate MOBLO problems as a constrained multi-objective optimization (MOO) problem via the value-function approach. Then we propose a novel multi-gradient aggregation method to solve the challenging constrained MOO problem. Theoretically, we provide the complexity analysis to show the efficiency of the proposed method and a non-asymptotic convergence result. Empirically, extensive experiments demonstrate the effectiveness and efficiency of the proposed FORUM method in different learning problems. In particular, it achieves state-of-the-art performance on three multi-task learning benchmark datasets. The code is available at https://github.com/Baijiong-Lin/FORUM.

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