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Adaptive moment methods have been remarkably successful in deep learning optimization, particularly in the presence of noisy and/or sparse gradients. We further the advantages of adaptive moment techniques by proposing a family of double…

Machine Learning · Statistics 2018-11-07 Kin Gutierrez , Jin Li , Cristian Challu , Artur Dubrawski

Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…

Optimization and Control · Mathematics 2025-04-08 Zhishuai Guo , Yi Xu , Wotao Yin , Rong Jin , Tianbao Yang

In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…

Optimization and Control · Mathematics 2026-03-24 Edoardo Cesaroni , Giampaolo Liuzzi , Stefano Lucidi

Tuning step sizes is crucial for the stability and efficiency of optimization algorithms. While adaptive coordinate-wise step sizes have been shown to outperform scalar step size in first-order methods, their use in second-order methods is…

Machine Learning · Computer Science 2025-05-20 Wei Lin , Qingyu Song , Hong Xu

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…

Optimization and Control · Mathematics 2024-07-15 Mathieu Besançon , Miguel F. Anjos , Luce Brotcorne

Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential…

Machine Learning · Computer Science 2023-03-01 Francesco Alesiani

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Optimization and Control · Mathematics 2019-07-18 Mostafa Amini , Farzad Yousefian

Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…

Optimization and Control · Mathematics 2024-12-25 Quan Xiao , Tianyi Chen

Many important machine learning applications involve regularized nonconvex bi-level optimization. However, the existing gradient-based bi-level optimization algorithms cannot handle nonconvex or nonsmooth regularizers, and they suffer from…

Machine Learning · Computer Science 2022-06-06 Ziyi Chen , Bhavya Kailkhura , Yi Zhou

This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient…

Optimization and Control · Mathematics 2026-05-12 Linjing Chen , Antai Xie , Xinlei Yi , Xiaoqiang Ren , Xiaofan Wang

Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple…

Optimization and Control · Mathematics 2023-10-09 Quan Xiao , Songtao Lu , Tianyi Chen

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…

Optimization and Control · Mathematics 2025-06-10 Lea Bogensperger , Matthias J. Ehrhardt , Thomas Pock , Mohammad Sadegh Salehi , Hok Shing Wong

We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…

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

We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…

Optimization and Control · Mathematics 2025-01-31 Pavel Dvurechensky , Gabriele Iommazzo , Shimrit Shtern , Mathias Staudigl

While LLMs excel at single-turn generation, they struggle with long-horizon, multi-turn interactions. Offline reinforcement learning (RL) offers a scalable approach, yet its performance hinges on the availability and quality of multi-turn…

Machine Learning · Computer Science 2026-05-26 Shresth Verma , Mauricio Tec , Cheol Woo Kim , Kai Wang , Milind Tambe

In this paper, we explore a specific optimization problem that combines a differentiable nonconvex function with a nondifferentiable function for multi-block variables, which is particularly relevant to tackle the multilinear…

Optimization and Control · Mathematics 2025-01-10 Zehui Liu , Qingsong Wang , Chunfeng Cui

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…

Optimization and Control · Mathematics 2025-02-28 Yan Yang , Bin Gao , Ya-xiang Yuan

Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively…

Optimization and Control · Mathematics 2025-04-22 Guy Kornowski , Swati Padmanabhan , Kai Wang , Zhe Zhang , Suvrit Sra

Trilevel learning, also called trilevel optimization (TLO), has been recognized as a powerful modelling tool for hierarchical decision process and widely applied in many machine learning applications, such as robust neural architecture…

Machine Learning · Computer Science 2024-01-23 Yang Jiao , Kai Yang , Tiancheng Wu , Chengtao Jian , Jianwei Huang