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Bilevel optimization has recently attracted significant attention in machine learning due to its wide range of applications and advanced hierarchical optimization capabilities. In this paper, we propose a plug-and-play framework, named…

Optimization and Control · Mathematics 2025-05-05 Tianshu Chu , Dachuan Xu , Wei Yao , Chengming Yu , Jin Zhang

Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic -- primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms…

Machine Learning · Computer Science 2024-02-08 Sungduk Yu , Mike Pritchard , Po-Lun Ma , Balwinder Singh , Sam Silva

Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces…

Machine Learning · Computer Science 2023-02-14 Julia Moosbauer , Giuseppe Casalicchio , Marius Lindauer , Bernd Bischl

We propose a bilevel optimization strategy for selecting the best hyperparameter value for the nonsmooth $\ell_p$ regularizer with $0<p\le 1$. The concerned bilevel optimization problem has a nonsmooth, possibly nonconvex,…

Optimization and Control · Mathematics 2021-12-20 Takayuki Okuno , Akiko Takeda , Akihiro Kawana , Motokazu Watanabe

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

Hyperparameter optimization (HPO) is a critical component of machine learning pipelines, significantly affecting model robustness, stability, and generalization. However, HPO is often a time-consuming and computationally intensive task.…

Machine Learning · Computer Science 2025-03-10 Ruinan Wang , Ian Nabney , Mohammad Golbabaee

Bilevel optimization is widely applied in many machine learning tasks such as hyper-parameter learning, meta learning and reinforcement learning. Although many algorithms recently have been developed to solve the bilevel optimization…

Optimization and Control · Mathematics 2024-07-26 Feihu Huang

Preference optimization methods typically begin training with a well-trained SFT model as a reference model. In RLHF and DPO, a regularization term is used during the preference optimization process to prevent the policy model from…

Computation and Language · Computer Science 2024-09-30 Cheolhun Jang

Policy gradient methods usually rely on entropy regularization to prevent premature convergence. However, maximizing entropy indiscriminately pushes the policy towards a uniform distribution, often overriding the reward signal if not…

Machine Learning · Computer Science 2026-03-06 Luca Serfilippi , Giorgio Franceschelli , Antonio Corradi , Mirco Musolesi

In this paper, we study a class of bilevel optimization problems where the lower-level problem is a convex composite optimization model, which arises in various applications, including bilevel hyperparameter selection for regularized…

Optimization and Control · Mathematics 2026-05-13 Xiaoning Bai , Shangzhi Zeng , Jin Zhang , Lezhi Zhang

Because of its sample efficiency, Bayesian optimization (BO) has become a popular approach dealing with expensive black-box optimization problems, such as hyperparameter optimization (HPO). Recent empirical experiments showed that the loss…

Machine Learning · Computer Science 2021-11-11 Difan Deng , Marius Lindauer

Bayesian Optimization (BO) is a common approach for hyperparameter optimization (HPO) in automated machine learning. Although it is well-accepted that HPO is crucial to obtain well-performing machine learning models, tuning BO's own…

Machine Learning · Computer Science 2019-08-20 Marius Lindauer , Matthias Feurer , Katharina Eggensperger , André Biedenkapp , Frank Hutter

We consider the solution to the biharmonic equation in mixed form discretized by the Hybrid High-Order (HHO) methods. The two resulting second-order elliptic problems can be decoupled via the introduction of a new unknown, corresponding to…

Numerical Analysis · Mathematics 2024-09-06 Paola F. Antonietti , Pierre Matalon , Marco Verani

Given a Hyperparameter Optimization(HPO) problem, how to design an algorithm to find optimal configurations efficiently? Bayesian Optimization(BO) and the multi-fidelity BO methods employ surrogate models to sample configurations based on…

Machine Learning · Computer Science 2024-02-22 Yang Zhang , Haiyang Wu , Yuekui Yang

This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…

Optimization and Control · Mathematics 2025-10-07 Shimrit Shtern , Adeolu Taiwo

As machine learning permeates more industries and models become more expensive and time consuming to train, the need for efficient automated hyperparameter optimization (HPO) has never been more pressing. Multi-step planning based…

Machine Learning · Computer Science 2022-11-18 Lucio M. Dery , Abram L. Friesen , Nando De Freitas , Marc'Aurelio Ranzato , Yutian Chen

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

Large Language Models (LLMs) have shown great potential in automatically generating and optimizing (meta)heuristics, making them valuable tools in heuristic optimization tasks. However, LLMs are generally inefficient when it comes to…

Neural and Evolutionary Computing · Computer Science 2025-05-23 Niki van Stein , Diederick Vermetten , Thomas Bäck

Subspace optimization methods have the attractive property of reducing large-scale optimization problems to a sequence of low-dimensional subspace optimization problems. However, existing subspace optimization frameworks adopt a fixed…

Optimization and Control · Mathematics 2022-03-03 Yoni Choukroun , Michael Katz

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