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We propose a novel approach for analyzing dynamic regret of first-order constrained online convex optimization algorithms for strongly convex and Lipschitz-smooth objectives. Crucially, we provide a general analysis that is applicable to a…

Optimization and Control · Mathematics 2025-08-22 Fabian Jakob , Andrea Iannelli

Bilevel optimization has become a powerful tool in a wide variety of machine learning problems. However, the current nonconvex bilevel optimization considers an offline dataset and static functions, which may not work well in emerging…

Optimization and Control · Mathematics 2023-11-10 Sen Lin , Daouda Sow , Kaiyi Ji , Yingbin Liang , Ness Shroff

We study online convex optimization with constraints consisting of multiple functional constraints and a relatively simple constraint set, such as a Euclidean ball. As enforcing the constraints at each time step through projections is…

Optimization and Control · Mathematics 2022-12-06 Shuang Qiu , Xiaohan Wei , Mladen Kolar

Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex…

Machine Learning · Computer Science 2025-11-27 Kaiyi Ji

This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for online single-level algorithms to the bilevel setting.…

Optimization and Control · Mathematics 2024-07-10 Davoud Ataee Tarzanagh , Parvin Nazari , Bojian Hou , Li Shen , Laura Balzano

Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications, such as online auction, network revenue management, order fulfillment and advertising. Existing OLP…

Data Structures and Algorithms · Computer Science 2025-11-18 Guokai Li , Zizhuo Wang , Jingwei Zhang

This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…

Optimization and Control · Mathematics 2024-07-16 Liam Madden , Stephen Becker , Emiliano Dall'Anese

We revisit the challenge of designing online algorithms for the bandit convex optimization problem (BCO) which are also scalable to high dimensional problems. Hence, we consider algorithms that are \textit{projection-free}, i.e., based on…

Machine Learning · Computer Science 2019-10-09 Dan Garber , Ben Kretzu

In this paper, we propose an online convex optimization approach with two different levels of adaptivity. On a higher level, our approach is agnostic to the unknown types and curvatures of the online functions, while at a lower level, it…

Machine Learning · Computer Science 2024-04-17 Yu-Hu Yan , Peng Zhao , Zhi-Hua Zhou

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…

Optimization and Control · Mathematics 2026-05-11 Yiyang Shen , Yutian He , Weiran Wang , Qihang Lin

A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…

Optimization and Control · Mathematics 2026-03-11 Serge Gratton , Philippe L. Toint

To address the uncertainty in function types, recent progress in online convex optimization (OCO) has spurred the development of universal algorithms that simultaneously attain minimax rates for multiple types of convex functions. However,…

Machine Learning · Computer Science 2024-05-31 Wenhao Yang , Yibo Wang , Peng Zhao , Lijun Zhang

In this paper, we introduce a new projection-free algorithm for Online Convex Optimization (OCO) with a state-of-the-art regret guarantee among separation-based algorithms. Existing projection-free methods based on the classical Frank-Wolfe…

Machine Learning · Computer Science 2024-10-08 Zakaria Mhammedi

In Online Convex Optimization (OCO), when the stochastic gradient has a finite variance, many algorithms provably work and guarantee a sublinear regret. However, limited results are known if the gradient estimate has a heavy tail, i.e., the…

Machine Learning · Computer Science 2026-03-20 Zijian Liu

A well-studied generalization of the standard online convex optimization (OCO) framework is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the…

Machine Learning · Computer Science 2024-10-29 Abhishek Sinha , Rahul Vaze

We consider online convex optimization with a zero-order oracle feedback. In particular, the decision maker does not know the explicit representation of the time-varying cost functions, or their gradients. At each time step, she observes…

Optimization and Control · Mathematics 2020-05-05 Tatiana Tatarenko , Maryam Kamgarpour

This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…

Optimization and Control · Mathematics 2025-11-18 Cac Phan , Kai Wang

In this paper, we develop a novel virtual-queue-based online algorithm for online convex optimization (OCO) problems with long-term and time-varying constraints and conduct a performance analysis with respect to the dynamic regret and…

Optimization and Control · Mathematics 2021-11-16 Qingsong Liu , Wenfei Wu , Longbo Huang , Zhixuan Fang

We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…

Optimization and Control · Mathematics 2022-09-14 Hakan Gokcesu , Suleyman S. Kozat

We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions $\f_t$ admit a "pseudo-1d" structure, i.e. $\f_t(\w) = \loss_t(\pred_t(\w))$ where the output of $\pred_t$ is…

Machine Learning · Computer Science 2021-02-16 Aadirupa Saha , Nagarajan Natarajan , Praneeth Netrapalli , Prateek Jain