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In this paper, we study the Multi-Objective Bi-Level Optimization (MOBLO)problem, where the upper-level subproblem is a multi-objective optimizationproblem and the lower-level subproblem is for scalar optimization. Existinggradient-based MOBLO algorithms need to compute the Hessian matrix, causing thecomputational inefficient problem. To address this, we propose an efficientfirst-order multi-gradient method for MOBLO, called FORUM. Specifically, wereformulate MOBLO problems as a constrained multi-objective optimization (MOO)problem via the value-function approach. Then we propose a novel multi-gradientaggregation method to solve the challenging constrained MOO problem.Theoretically, we provide the complexity analysis to show the efficiency of theproposed method and a non-asymptotic convergence result. Empirically, extensiveexperiments demonstrate the effectiveness and efficiency of the proposed FORUMmethod in different learning problems. In particular, it achievesstate-of-the-art performance on three multi-task learning benchmark datasets.

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