相关论文: Optimal Projection Filters

We consider the classical setting of optimizing a nonsmooth Lipschitz continuous convex function over a convex constraint set, when having access to a (stochastic) first-order oracle (FO) for the function and a projection oracle (PO) for…

The dynamics in a primary Spectral Submanifold (SSM) constructed over the slowest modes of a dynamical system provide an ideal reduced-order model for nearby trajectories. Modeling the dynamics of trajectories further away from the primary…

In this work, we present an efficient gradient projection method for solving a class of stochastic optimal control problem with expected integral state constraint. The first order optimality condition system consisting of forward-backward…

The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…

Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…

The best uniform rational approximation of the \emph{sign} function on two intervals separated by zero was explicitly solved by E.I. Zolotar\"ev in 1877. This optimization problem is the initial step in the staircase of the so called…

We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…

A key challenge in topology optimization (TopOpt) is that manufacturable structures, being inherently binary, are non-differentiable, creating a fundamental tension with gradient-based optimization. The subpixel-smoothed projection (SSP)…

We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the classic book by Kushner and Yin. Using the ODE method, we…

Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…

We study how stochastic differential equation (SDE) based ideas can inspire new modifications to existing algorithms for a set of problems in computer vision. Loosely speaking, our formulation is related to both explicit and implicit…

We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…

We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show…

The problem of the Taylor-Ito and Taylor-Stratonovich expansions of the Ito stochastic processes in a neighborhood of a fixed moment of time is considered. The classical forms of the Taylor-Ito and Taylor-Stratonovich expansions are…

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

What is the optimal way to approximate a high-dimensional diffusion process by one in which the coordinates are independent? This paper presents a construction, called the \emph{independent projection}, which is optimal for two natural…

We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic…

We present the first mathematical analysis of stochastic density functional theory (DFT) in the context of the Hartree approximation. We motivate our analysis via the notion of nearly-optimal or $\tilde{O}(n)$ scaling with respect to the…

Direct Preference Optimization (DPO) aligns text-to-image (T2I) generation models with human preferences using pairwise preference data. Although substantial resources are expended in collecting and labeling datasets, a critical aspect is…