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Design optimisation offers the potential to develop lightweight aircraft structures with reduced environmental impact. Due to the high number of design variables and constraints, these challenges are typically addressed using gradient-based…

Computational Engineering, Finance, and Science · Computer Science 2025-08-04 Hauke F. Maathuis , Roeland De Breuker , Saullo G. P. Castro

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

We discuss the design of an invariant measure-preserving transformed dynamics for the numerical treatment of Langevin dynamics based on rescaling of time, with the goal of sampling from an invariant measure. Given an appropriate monitor…

Numerical Analysis · Mathematics 2024-08-30 Alix Leroy , Benedict Leimkuhler , Jonas Latz , Desmond J. Higham

We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…

Optimization and Control · Mathematics 2020-03-12 Antonio Orvieto , Aurelien Lucchi

In this paper, we introduce a technique to enhance the computational efficiency of solution algorithms for high-dimensional discrete simulation-based optimization problems. The technique is based on innovative adaptive partitioning…

Optimization and Control · Mathematics 2024-12-04 Jing Lu , Tianli Zhou , Carolina Osorio

One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many…

Machine Learning · Computer Science 2018-08-02 Behnoosh Parsa , Keshav Rajasekaran , Franziska Meier , Ashis G. Banerjee

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…

Machine Learning · Statistics 2020-07-27 Tengyuan Liang , Weijie Su

This paper studies the fundamental problem of learning deep generative models that consist of multiple layers of latent variables organized in top-down architectures. Such models have high expressivity and allow for learning hierarchical…

Machine Learning · Statistics 2020-07-21 Erik Nijkamp , Bo Pang , Tian Han , Linqi Zhou , Song-Chun Zhu , Ying Nian Wu

We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for non-convex optimization. The algorithm performs stochastic gradient descent, where in each step it injects appropriately scaled Gaussian noise to the update. We analyze…

Machine Learning · Computer Science 2018-04-10 Yuchen Zhang , Percy Liang , Moses Charikar

We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…

Machine Learning · Computer Science 2020-02-14 Yixuan Qiu , Xiao Wang

Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…

Machine Learning · Statistics 2018-11-22 Dmitry Babichev , Francis Bach

Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

Optimization and Control · Mathematics 2025-05-20 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

Stochastic gradient Langevin dynamics (SGLD) has gained the attention of optimization researchers due to its global optimization properties. This paper proves an improved convergence property to local minimizers of nonconvex objective…

Machine Learning · Computer Science 2024-07-08 Zhishen Huang , Stephen Becker

We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…

Machine Learning · Computer Science 2022-04-29 Yunfei Teng , Wenbo Gao , Francois Chalus , Anna Choromanska , Donald Goldfarb , Adrian Weller

Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…

Artificial Intelligence · Computer Science 2023-07-19 Yunwen Lei

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Machine Learning · Statistics 2018-11-19 Patrick Chao , Tahereh Mazaheri , Bo Sun , Nicholas B. Weingartner , Zohar Nussinov

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

Optimization and Control · Mathematics 2020-05-05 Quoc Tran-Dinh , Nhan H. Pham , Dzung T. Phan , Lam M. Nguyen

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters…

We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…

Optimization and Control · Mathematics 2025-06-11 Qi Feng , Gu Wang

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…

Machine Learning · Computer Science 2022-10-11 Siqi Liang , Yan Sun , Faming Liang