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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

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

Optimization and Control · Mathematics 2018-11-13 Aryan Mokhtari , Hamed Hassani , Amin Karbasi

Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…

Optimization and Control · Mathematics 2025-01-17 Zhichao Jia , Benjamin Grimmer

A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity…

Optimization and Control · Mathematics 2025-01-22 Serge Gratton , Sadok Jerad , Philippe L. Toint

In this paper, we propose the Bi-Sub-Gradient (Bi-SG) method, which is a generalization of the classical sub-gradient method to the setting of convex bi-level optimization problems. This is a first-order method that is very easy to…

Optimization and Control · Mathematics 2023-07-18 Roey Merchav , Shoham Sabach

In this paper, we revisit the bilevel optimization problem, in which the upper-level objective function is generally nonconvex and the lower-level objective function is strongly convex. Although this type of problem has been studied…

Optimization and Control · Mathematics 2025-04-08 Yifan Yang , Peiyao Xiao , Kaiyi Ji

Several important problem settings within the literature of reinforcement learning (RL), such as meta-learning, hierarchical learning, and RL from human feedback (RL-HF), can be modelled as bilevel RL problems. A lot has been achieved in…

Machine Learning · Computer Science 2026-02-03 Naman Saxena , Vaneet Aggarwal

In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…

Optimization and Control · Mathematics 2019-10-10 Andrei Kulunchakov , Julien Mairal

Bilevel optimization is a popular two-level hierarchical optimization, which has been widely applied to many machine learning tasks such as hyperparameter learning, meta learning and continual learning. Although many bilevel optimization…

Optimization and Control · Mathematics 2023-11-21 Feihu Huang

Bilevel optimization (BLO) is a popular approach with many applications including hyperparameter optimization, neural architecture search, adversarial robustness and model-agnostic meta-learning. However, the approach suffers from time and…

Machine Learning · Computer Science 2021-06-08 Valerii Likhosherstov , Xingyou Song , Krzysztof Choromanski , Jared Davis , Adrian Weller

Bilevel optimization is one of the fundamental problems in machine learning and optimization. Recent theoretical developments in bilevel optimization focus on finding the first-order stationary points for nonconvex-strongly-convex cases. In…

Machine Learning · Computer Science 2023-05-11 Minhui Huang , Xuxing Chen , Kaiyi Ji , Shiqian Ma , Lifeng Lai

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

Machine Learning · Computer Science 2015-07-28 Elad Hazan , Kfir Y. Levy , Shai Shalev-Shwartz

We investigate a class of nonconvex optimization problems characterized by a feasible set consisting of level-bounded nonconvex regularizers, with a continuously differentiable objective. We propose a novel hybrid approach to tackle such…

Optimization and Control · Mathematics 2024-10-28 Xiangyu Yang , Hao Wang , Yichen Zhu , Xiao Wang

In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual…

Optimization and Control · Mathematics 2022-11-22 Quanqi Hu , Yongjian Zhong , Tianbao Yang

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

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

Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…

Optimization and Control · Mathematics 2016-02-05 Aleksandr Y. Aravkin , James V. Burke , Dmitriy Drusvyatskiy , Michael P. Friedlander , Scott Roy

Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…

Optimization and Control · Mathematics 2024-11-12 Junyi Li , Heng Huang

Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the…

Machine Learning · Statistics 2023-01-10 Enrico Crovini , Simon L. Cotter , Konstantinos Zygalakis , Andrew B. Duncan

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
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