Related papers: Multi-level Monte-Carlo Gradient Methods for Stoch…
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
We introduce Multi-Iteration Stochastic Optimizers, a novel class of first-order stochastic methods that control the relative $L^2$ error using successive control variates along the iteration path. By exploiting correlations between…
In this paper, we consider non-convex stochastic bilevel optimization (SBO) problems that have many applications in machine learning. Although numerous studies have proposed stochastic algorithms for solving these problems, they are limited…
In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its…
Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They are theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that in…
While standard reinforcement learning optimizes a single reward signal, many applications require optimizing a nonlinear utility $f(J_1^\pi,\dots,J_M^\pi)$ over multiple objectives, where each $J_m^\pi$ denotes the expected discounted…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…
We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision…
We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin…
In this paper, we present new stochastic methods for solving two important classes of nonconvex optimization problems. We first introduce a randomized accelerated proximal gradient (RapGrad) method for solving a class of nonconvex…
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…
Real-world distributed systems and networks are often unreliable and subject to random failures of its components. Such a stochastic behavior affects adversely the complexity of optimization tasks performed routinely upon such systems, in…
In this paper we introduce new methods for convex optimization problems with inexact stochastic oracle. First method is an extension of the intermediate gradient method proposed by Devolder, Glineur and Nesterov for problems with inexact…
An optimal experimental set-up maximizes the value of data for statistical inferences and predictions. The efficiency of strategies for finding optimal experimental set-ups is particularly important for experiments that are time-consuming…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem…