Related papers: Smoothing Methods for Automatic Differentiation Ac…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
Recent results in non-convex stochastic optimization demonstrate the convergence of popular adaptive algorithms (e.g., AdaGrad) under the $(L_0, L_1)$-smoothness condition, but the rate of convergence is a higher-order polynomial in terms…
In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient…
Modern problems in AI or in numerical analysis require nonsmooth approaches with a flexible calculus. We introduce generalized derivatives called conservative fields for which we develop a calculus and provide representation formulas.…
Process reward models (PRMs) offer fine-grained, step-level evaluations that facilitate deeper reasoning processes in large language models (LLMs), proving effective in complex tasks like mathematical reasoning. However, developing PRMs is…
We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random…
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…
Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions…
We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…
Iso-surface extraction from an implicit field is a fundamental process in various applications of computer vision and graphics. When dealing with geometric shapes with complicated geometric details, many existing algorithms suffer from high…
We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…
The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization,…
Gradient clipping is a standard training technique used in deep learning applications such as large-scale language modeling to mitigate exploding gradients. Recent experimental studies have demonstrated a fairly special behavior in the…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
Implicit time integration schemes are widely used in computational fluid dynamics numerical codes to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step stability constraints than their explicit…
The automation of probabilistic reasoning is one of the primary aims of machine learning. Recently, the confluence of variational inference and deep learning has led to powerful and flexible automatic inference methods that can be trained…
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…
In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of…