Papers › Min-Max Bilevel Multi-objective Optimization with Applications in Machine Learning

Min-Max Bilevel Multi-objective Optimization with Applications in Machine Learning

3 Mar 2022arXiv:2203.01924archive 2025-07-28

Alex Gu, Songtao Lu, Parikshit Ram, Lily Weng

We consider a generic min-max multi-objective bilevel optimization problem with applications in robust machine learning such as representation learning and hyperparameter optimization. We design MORBiT, a novel single-loop gradient descent-ascent bilevel optimization algorithm, to solve the generic problem and present a novel analysis showing that MORBiT converges to the first-order stationary point at a rate of 𝒪(n^(1/2) K^(-2/5)) for a class of weakly convex problems with n objectives upon K iterations of the algorithm. Our analysis utilizes novel results to handle the non-smooth min-max multi-objective setup and to obtain a sublinear dependence in the number of objectives n. Experimental results on robust representation learning and robust hyperparameter optimization showcase (i) the advantages of considering the min-max multi-objective setup, and (ii) convergence properties of the proposed MORBiT. Our code is at https://github.com/minimario/MORBiT.

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