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We address the open problem of training hypernetworks for Controllable Pareto Front Learning (CPFL) under split feasibility conditions with rigorous theoretical guarantees. We reformulate the constrained Pareto problem as a Bi-Level…

Machine Learning · Computer Science 2026-05-20 Nguyen Viet Hoang , Dung D. Le , Tran Ngoc Thang

We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…

Optimization and Control · Mathematics 2025-08-27 Alberto De Marchi , Andreas Themelis

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

First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…

Optimization and Control · Mathematics 2024-02-07 Junyu Zhang , Mingyi Hong

Continual Learning (CL) aims to train neural networks on a dynamic stream of tasks without forgetting previously learned knowledge. Among optimization-based approaches, C-Flat has emerged as a promising solution due to its plug-and-play…

Machine Learning · Computer Science 2026-04-16 Wei Li , Hangjie Yuan , Zixiang Zhao , Borui Kang , Ziwei Liu , Tao Feng

Regularization techniques are crucial to improving the generalization performance and training efficiency of deep neural networks. Many deep learning algorithms rely on weight decay, dropout, batch/layer normalization to converge faster and…

Machine Learning · Computer Science 2025-05-23 Peng Lu , Ahmad Rashid , Ivan Kobyzev , Mehdi Rezagholizadeh , Philippe Langlais

The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…

Optimization and Control · Mathematics 2025-06-18 Lucka Barbeau , Marc-Étienne Lamarche-Gagnon , Florin Ilinca

In linear regression, SLOPE is a new convex analysis method that generalizes the Lasso via the sorted L1 penalty: larger fitted coefficients are penalized more heavily. This magnitude-dependent regularization requires an input of penalty…

Machine Learning · Statistics 2021-12-14 Yiliang Zhang , Zhiqi Bu

Bilevel optimization problems, encountered in fields such as economics, engineering, and machine learning, pose significant computational challenges due to their hierarchical structure and constraints at both upper and lower levels.…

Optimization and Control · Mathematics 2024-08-21 Mengwei Xu , Yu-Hong Dai , Xin-Wei Liu , Bo Wang

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning…

Machine Learning · Computer Science 2013-03-20 Pinghua Gong , Changshui Zhang , Zhaosong Lu , Jianhua Huang , Jieping Ye

Fine-tuning Large Language Models (LLMs) typically involves either full fine-tuning, which updates all model parameters, or Parameter-Efficient Fine-Tuning (PEFT), which adjusts a small subset of parameters. However, both approaches have…

Artificial Intelligence · Computer Science 2026-04-14 Shaocong Ma , Peiran Yu , Heng Huang

Solving NP-hard constrained combinatorial optimization problems using quantum algorithms remains a challenging yet promising avenue toward quantum advantage. Variational Quantum Algorithms (VQAs), such as the Variational Quantum Eigensolver…

Quantum Physics · Physics 2025-07-28 Xin Wei Lee , Hoong Chuin Lau

Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…

Optimization and Control · Mathematics 2025-03-25 Sina Sharifi , Nazanin Abolfazli , Erfan Yazdandoost Hamedani , Mahyar Fazlyab

We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…

Optimization and Control · Mathematics 2021-11-08 Jonathan Kelner , Annie Marsden , Vatsal Sharan , Aaron Sidford , Gregory Valiant , Honglin Yuan

We consider the constrained sampling problem where the goal is to sample from a target distribution $\pi(x)\propto e^{-f(x)}$ when $x$ is constrained to lie on a convex body $\mathcal{C}$. Motivated by penalty methods from continuous…

Machine Learning · Statistics 2025-05-16 Mert Gürbüzbalaban , Yuanhan Hu , Lingjiong Zhu

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…

Machine Learning · Computer Science 2023-03-16 Meng Ding , Mingxi Lei , Yunwen Lei , Di Wang , Jinhui Xu

Uncertainties in transition dynamics pose a critical challenge in reinforcement learning (RL), often resulting in performance degradation of trained policies when deployed on hardware. Many robust RL approaches follow two strategies:…

Machine Learning · Computer Science 2026-01-29 Xulin Chen , Ruipeng Liu , Zhenyu Gan , Garrett E. Katz

This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…

Optimization and Control · Mathematics 2024-03-06 Jiulin Wang , Xu Shi , Rujun Jiang

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

Optimization and Control · Mathematics 2021-08-10 Tom Tirer , Raja Giryes

We consider the problem of minimizing a convex separable objective (as a separable sum of two proper closed convex functions $f$ and $g$) over a linear coupling constraint. We assume that $f$ can be decomposed as the sum of a smooth part…

Optimization and Control · Mathematics 2025-07-29 Hao Zhang , Liaoyuan Zeng , Ting Kei Pong