相关论文: General multilevel adaptations for stochastic appr…

This paper presents a novel approach to level set estimation for any function/simulation with an arbitrary number of continuous inputs and arbitrary numbers of continuous responses. We present a method that uses existing data from computer…

Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the…

In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard…

In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to…

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…

In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use…

The paper considers a class of parametric elliptic partial differential equations (PDEs), where the coefficients and the right-hand side function depend on infinitely many (uncertain) parameters. We introduce a two-level a posteriori…

In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…

Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step,…

We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed:…

In this paper, we study and analyze zeroth-order stochastic approximation algorithms for solving bilvel problems, when neither the upper/lower objective values, nor their unbiased gradient estimates are available. In particular, exploiting…

The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…

We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with…

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…

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…

We introduce three related but distinct improvements to multilevel Monte Carlo (MLMC) methods for the solution of systems of stochastic differential equations (SDEs). Firstly, we show that when the payoff function is twice continuously…

This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…