Feb. 13, 2024, 5:45 a.m. | Jeongyeol Kwon Dohyun Kwon Stephen Wright Robert Nowak

cs.LG updates on arXiv.org arxiv.org

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter $\sigma > 0$. In particular, we establish a strong connection between the penalty function and …

algorithms approximation cs.lg functions landscape math.oc optimization stochastic study through variables work

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