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Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

Multiagent Systems · Computer Science 2017-12-12 Yang Yang , Gesualdo Scutari , Daniel P. Palomar , Marius Pesavento

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine…

Machine Learning · Computer Science 2026-05-26 Xinwen Zhang , Yihan Zhang , Heng Liang , Hongchang Gao

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

In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem…

Machine Learning · Computer Science 2022-10-20 Wei Jiang , Bokun Wang , Yibo Wang , Lijun Zhang , Tianbao Yang

Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…

Machine Learning · Computer Science 2023-03-28 Hongchang Gao , Bin Gu , My T. Thai

Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

Optimization and Control · Mathematics 2025-05-20 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…

Optimization and Control · Mathematics 2025-10-13 Hantao Nie , Jiaxiang Li , Zaiwen Wen

Adam has become one of the most popular optimizers for training modern deep neural networks, such as transformers. However, its applicability is largely restricted to single-level optimization problems. In this paper, we aim to extend…

Machine Learning · Computer Science 2025-03-07 Xiaochuan Gong , Jie Hao , Mingrui Liu

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

Optimization and Control · Mathematics 2017-05-23 Xiao Wang , Shiqian Ma , Donald Goldfarb , Wei Liu

Contextual Stochastic Bilevel Optimization (CSBO) extends standard stochastic bilevel optimization (SBO) by incorporating context-dependent lower-level problems. CSBO problems are generally intractable since existing methods require solving…

Optimization and Control · Mathematics 2025-10-07 Maxime Bouscary , Jiawei Zhang , Saurabh Amin

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

Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…

Machine Learning · Computer Science 2025-10-27 Xiaochuan Gong , Jie Hao , Mingrui Liu

Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…

Optimization and Control · Mathematics 2022-06-14 Xuxing Chen , Minhui Huang , Shiqian Ma

Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…

Optimization and Control · Mathematics 2015-09-16 Qi Deng , Guanghui Lan , Anand Rangarajan

Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…

Optimization and Control · Mathematics 2026-02-10 Yin Liu , Sam Davanloo Tajbakhsh

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…

Optimization and Control · Mathematics 2021-06-16 Prashant Khanduri , Siliang Zeng , Mingyi Hong , Hoi-To Wai , Zhaoran Wang , Zhuoran Yang

In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming…

Optimization and Control · Mathematics 2025-04-17 Stephan Dempe , Joydeep Duta , Tanushree Pandit , K. S. Mallikarjuna Rao

Bilevel optimization has been recently used in many machine learning problems such as hyperparameter optimization, policy optimization, and meta learning. Although many bilevel optimization methods have been proposed, they still suffer from…

Optimization and Control · Mathematics 2022-10-27 Feihu Huang , Junyi Li , Shangqian Gao , Heng Huang

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

Optimization and Control · Mathematics 2023-03-28 Dmitry A. Pasechnyuk , Alexander Gornov

This paper studies the problem of stochastic bilevel optimization where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level function is strongly convex. This problem is motivated by meta-learning…

Machine Learning · Computer Science 2024-12-31 Xiaochuan Gong , Jie Hao , Mingrui Liu