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Data augmentation is a key practice in machine learning for improving generalization performance. However, finding the best data augmentation hyperparameters requires domain knowledge or a computationally demanding search. We address this…

Computer Vision and Pattern Recognition · Computer Science 2020-11-11 Saypraseuth Mounsaveng , Issam Laradji , Ismail Ben Ayed , David Vazquez , Marco Pedersoli

Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…

Machine Learning · Computer Science 2022-06-22 Jonathan Wenger , Geoff Pleiss , Philipp Hennig , John P. Cunningham , Jacob R. Gardner

Hyperparameter optimization aims to find the optimal hyperparameter configuration of a machine learning model, which provides the best performance on a validation dataset. Manual search usually leads to get stuck in a local hyperparameter…

Machine Learning · Statistics 2018-11-01 Jungtaek Kim , Saehoon Kim , Seungjin Choi

Gradient-based hyperparameter optimization (HPO) have emerged recently, leveraging bilevel programming techniques to optimize hyperparameter by estimating hypergradient w.r.t. validation loss. Nevertheless, previous theoretical works mainly…

Machine Learning · Computer Science 2026-02-23 Yubo Zhou , Jun Shu , Junmin Liu , Deyu Meng

Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…

Optimization and Control · Mathematics 2022-06-14 Xuxing Chen , Minhui Huang , Shiqian Ma

Optimization of hyper-parameters in reinforcement learning (RL) algorithms is a key task, because they determine how the agent will learn its policy by interacting with its environment, and thus what data is gathered. In this work, an…

Machine Learning · Computer Science 2019-09-19 Juan Cruz Barsce , Jorge A. Palombarini , Ernesto Martínez

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…

Machine Learning · Statistics 2013-10-28 Roman Garnett , Michael A. Osborne , Philipp Hennig

We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…

Numerical Analysis · Mathematics 2020-01-08 Vít Dolejší , Petr Tichý

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

Optimization and Control · Mathematics 2023-10-04 Xiaoxue Jiang

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Machine Learning · Statistics 2022-11-07 Vidhi Lalchand , Wessel P. Bruinsma , David R. Burt , Carl E. Rasmussen

Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…

Hyperparameter optimization of neural networks can be elegantly formulated as a bilevel optimization problem. While research on bilevel optimization of neural networks has been dominated by implicit differentiation and unrolling,…

Machine Learning · Computer Science 2020-10-27 Juhan Bae , Roger Grosse

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

Optimization and Control · Mathematics 2024-11-05 Pengyu Chen , Xu Shi , Rujun Jiang , Jiulin Wang

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…

Numerical Analysis · Mathematics 2021-08-26 Junyang Wang , Jon Cockayne , Oksana Chkrebtii , T. J. Sullivan , Chris. J. Oates

Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta-learning, continual learning, and reinforcement learning. Conventional BO…

Machine Learning · Computer Science 2022-09-20 Mao Ye , Bo Liu , Stephen Wright , Peter Stone , Qiang Liu

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Numerical Analysis · Mathematics 2024-03-20 Janina E. Schütte , Martin Eigel

In this thesis, we disentangle the generalized Gauss-Newton and approximate inference for Bayesian deep learning. The generalized Gauss-Newton method is an optimization method that is used in several popular Bayesian deep learning…

Machine Learning · Statistics 2020-07-24 Alexander Immer

Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen…

Numerical Analysis · Mathematics 2024-02-05 Xiaokai Huo , Hailiang Liu

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Machine Learning · Computer Science 2023-08-22 Siyuan Xu , Minghui Zhu

Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongly depends on loss function design, including the choice of…

Numerical Analysis · Mathematics 2025-03-13 Hee Jun Yang , Alexander Heinlein , Hyea Hyun Kim