Related papers: Monte-Carlo optimizations for resource allocation …

In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem. From the perspective of two optimization problems, i.e.,…

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…

We consider a network whose links have random capacities and in which a certain target amount of flow must be carried from some source nodes to some destination nodes. Each destination node has a fixed demand that must be satisfied and each…

We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to…

Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using…

An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…

We introduce bounds on the finite-time performance of Markov chain Monte Carlo algorithms in approaching the global solution of stochastic optimization problems over continuous domains. A comparison with other state-of-the-art methods…

This paper aims to motivate stochastic optimization problems from a statistical perspective and a statistical learning perspective, where the goal is to maximize the log-likelihood or minimize the population risk. We briefly describe the…

This paper proposes an analytical framework for modelling resource contention in multi-robot systems, where the travel times and task durations are uncertain. It uses several approximation methods to quickly and accurately calculate the…

Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…

The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…

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…

Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…

We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…

In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by find a…