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This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in…

Optimization and Control · Mathematics 2024-05-24 Haitong Liu , Qiang Li , Hoi-To Wai

This paper deals with stochastic optimization problems involving Markovian noise with a zero-order oracle. We present and analyze a novel derivative-free method for solving such problems in strongly convex smooth and non-smooth settings…

Optimization and Control · Mathematics 2026-01-06 Boris Prokhorov , Semyon Chebykin , Alexander Gasnikov , Aleksandr Beznosikov

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced…

Optimization and Control · Mathematics 2019-06-13 Hadrien Hendrikx , Francis Bach , Laurent Massoulie

In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied…

Numerical Analysis · Mathematics 2025-10-21 Christian Beck , Sebastian Becker , Patrick Cheridito , Arnulf Jentzen , Ariel Neufeld

Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…

Numerical Analysis · Mathematics 2020-08-04 Ruisheng Qi , Xiaojie Wang

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…

Machine Learning · Computer Science 2024-10-07 Yanfang Liu , Yuan Chen , Dongbin Xiu , Guannan Zhang

We propose an unbiased Monte-Carlo estimator for $\mathbb{E}[g(X_{t_1}, \cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a…

Probability · Mathematics 2016-03-08 Pierre Henry-Labordere , Xiaolu Tan , Nizar Touzi

This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…

Numerical Analysis · Mathematics 2025-06-03 Julian Andrej , Tzanio Kolev , Boyan Lazarov

Stochastic approximation (SA) algorithms are widely used in system optimization problems when only noisy measurements of the system are available. This paper studies two types of SA algorithms in a multivariate Kiefer-Wolfowitz setting:…

Optimization and Control · Mathematics 2021-07-28 Yiwen Chen

We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…

Machine Learning · Statistics 2023-10-03 Hong Ye Tan , Stanley Osher , Wuchen Li

We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…

Numerical Analysis · Mathematics 2007-05-23 Dongbin Xiu , Ioannis Kevrekidis

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…

Machine Learning · Computer Science 2020-05-19 Dhruv Malik , Ashwin Pananjady , Kush Bhatia , Koulik Khamaru , Peter L. Bartlett , Martin J. Wainwright

In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum…

Quantum Physics · Physics 2013-02-19 Xiaoting Wang , Mark Byrd , Kurt Jacobs

In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong…

Numerical Analysis · Mathematics 2025-10-21 Jingtao Zhu , Yuying Zhao , Siqing Gan

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced…

Optimization and Control · Mathematics 2020-05-22 Hadrien Hendrikx , Francis Bach , Laurent Massoulie

We present and analyze a stochastic distributed method (S-NEAR-DGD) that can tolerate inexact computation and inaccurate information exchange to alleviate the problems of costly gradient evaluations and bandwidth-limited communication in…

Optimization and Control · Mathematics 2021-02-02 Charikleia Iakovidou , Ermin Wei

We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly…

Machine Learning · Statistics 2013-01-08 David Wingate , Theophane Weber

We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. This problem was studied by, for instance, Gradinaru-Nourdin…

Probability · Mathematics 2019-11-27 Shigeki Aida , Nobuaki Naganuma

We study the approximation of expectations $\operatorname{E}(f(X))$ for solutions $X$ of stochastic differential equations and functionals $f$ on the path space by means of Monte Carlo algorithms that only use random bits instead of random…

Numerical Analysis · Mathematics 2023-01-10 Michael B. Giles , Mario Hefter , Lukas Mayer , Klaus Ritter

We consider the minimum makespan problem for $n$ tasks and two unrelated parallel selfish machines. Let $R_n$ be the best approximation ratio of randomized monotone scale-free algorithms. This class contains the most efficient algorithms…

Optimization and Control · Mathematics 2019-09-26 Olga Kuryatnikova , Juan C. Vera