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This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant…

Machine Learning · Computer Science 2025-01-16 Xiaochuan Gong , Jie Hao , Mingrui Liu

Stochastic Bilevel optimization usually involves minimizing an upper-level (UL) function that is dependent on the arg-min of a strongly-convex lower-level (LL) function. Several algorithms utilize Neumann series to approximate certain…

Optimization and Control · Mathematics 2023-06-22 Xuxing Chen , Tesi Xiao , Krishnakumar Balasubramanian

We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…

Optimization and Control · Mathematics 2025-09-29 Khanh-Hung Giang-Tran , Nam Ho-Nguyen , Fatma Kılınç-Karzan , Lingqing Shen

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem's domain X the sum…

Optimization and Control · Mathematics 2015-10-05 Bruce Cox , Anatoli Juditsky , Arkadi Nemirovski

This paper considers the smooth bilevel optimization in which the lower-level problem is strongly convex and the upper-level problem is possibly nonconvex. We focus on the stochastic setting where the algorithm can access the unbiased…

Machine Learning · Computer Science 2025-12-16 Zhuanghua Liu , Luo Luo

In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…

Optimization and Control · Mathematics 2021-07-14 Masoud Ahookhosh , Yurii Nesterov

Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…

Optimization and Control · Mathematics 2025-12-19 Dan Garber

Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…

Optimization and Control · Mathematics 2024-06-05 Wei Yao , Haian Yin , Shangzhi Zeng , Jin Zhang

Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient…

Optimization and Control · Mathematics 2026-02-04 Qichao Cao , Shangzhi Zeng , Jin Zhang

In this paper, we focus on the nonconvex-nonconvex bilevel optimization problem (BLO), where both upper-level and lower-level objectives are nonconvex, with the upper-level problem potentially being nonsmooth. We develop a two-timescale…

Optimization and Control · Mathematics 2026-04-24 Nachuan Xiao , Xiaoyin Hu , Xin Liu , Kim-Chuan Toh

In this paper we study a class of unconstrained and constrained bilevel optimization problems in which the lower level is a possibly nonsmooth convex optimization problem, while the upper level is a possibly nonconvex optimization problem.…

Optimization and Control · Mathematics 2024-03-08 Zhaosong Lu , Sanyou Mei

In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…

Optimization and Control · Mathematics 2025-03-14 Xiaotian Jiang , Jiaxiang Li , Mingyi Hong , Shuzhong Zhang

Nonconvex and nonsmooth bi-level optimization poses critical theoretical challenges, while arising in several applications. In this work, we develop a method for nonconvex, nonsmooth bi-level optimization and introduce Binno, a first-order…

Optimization and Control · Mathematics 2026-05-05 Laura Selicato , Flavia Esposito , Andersen Ang

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision…

Optimization and Control · Mathematics 2023-10-31 Yifan Hu , Jie Wang , Yao Xie , Andreas Krause , Daniel Kuhn

This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of…

Optimization and Control · Mathematics 2026-05-08 Sheng Yang , Chengchang Liu , Lesi Chen , John C. S. Lui

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

Optimization and Control · Mathematics 2019-12-17 Andreas Fischer , Alain B. Zemkoho , Shenglong Zhou

This paper considers a class of distributed bilevel optimization (DBO) problems with a coupled inner-level subproblem. Existing approaches typically rely on hypergradient estimations involving computationally expensive Hessian evaluation.…

Optimization and Control · Mathematics 2026-02-27 Youcheng Niu , Jinming Xu , Ying Sun , Li Chai , Jiming Chen

Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…

Machine Learning · Computer Science 2026-04-07 Xuelin Zhang , Hong Chen , Bin Gu , Tieliang Gong , Feng Zheng

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…

Optimization and Control · Mathematics 2016-01-14 V. Jeyakumar , J. B. Lasserre , G. Li , T. S. Pham

Bilevel optimization has found extensive applications in modern machine learning problems such as hyperparameter optimization, neural architecture search, meta-learning, etc. While bilevel problems with a unique inner minimal point (e.g.,…

Optimization and Control · Mathematics 2022-06-09 Daouda Sow , Kaiyi Ji , Ziwei Guan , Yingbin Liang