Related papers: Implicit Diffusion: Efficient Optimization through…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
This paper considers a problem where multiple users make repeated decisions based on their own observed events. The events and decisions at each time step determine the values of a utility function and a collection of penalty functions. The…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…
Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal…
This paper presents a joint optimisation framework for optimal estimation and stochastic optimal control with imperfect information. It provides a estimation and control scheme that can be decomposed into a classical optimal estimation step…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or…
This work develops effective distributed strategies for the solution of constrained multi-agent stochastic optimization problems with coupled parameters across the agents. In this formulation, each agent is influenced by only a subset of…
Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function $f$. We focus on stochastic functions that are given as an expectation of functions over a…
We revisit the asymptotic bias analysis of the distributed Pareto optimization algorithm developed based on the diffusion strategies. We propose an alternative way to analyze the asymptotic bias of this algorithm at small step-sizes and…
Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered. With these aims the asymptotic normality of sample covariance matrices for each strata is…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
Guided diffusion is a technique for conditioning the output of a diffusion model at sampling time without retraining the network for each specific task. One drawback of diffusion models, however, is their slow sampling process. Recent…