Related papers: Bandit-Based Monte Carlo Optimization for Nearest …
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
We give nearly-tight upper and lower bounds for the improving multi-armed bandits problem. An instance of this problem has $k$ arms, each of whose reward function is a concave and increasing function of the number of times that arm has been…
Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
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…
The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…
We consider the computation of the permanent of a binary n by n matrix. It is well- known that the exact computation is a #P complete problem. A variety of Markov chain Monte Carlo (MCMC) computational algorithms have been introduced in the…
Finding effective ways to exploit parallel computing to accelerate Markov chain Monte Carlo methods is an important problem in Bayesian computation and related disciplines. In this paper, we consider the zeroth-order setting where the…
We study the best-arm identification problem in multi-armed bandits with stochastic, potentially private rewards, when the goal is to identify the arm with the highest quantile at a fixed, prescribed level. First, we propose a (non-private)…
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…
Optimizing highly complex cost/energy functions over discrete variables is at the heart of many open problems across different scientific disciplines and industries. A major obstacle is the emergence of many-body effects among certain…
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…
We leverage multilevel Monte Carlo (MLMC) to improve the performance of multi-step look-ahead Bayesian optimization (BO) methods that involve nested expectations and maximizations. Often these expectations must be computed by Monte Carlo…
Many real-world functions are defined over both categorical and category-specific continuous variables and thus cannot be optimized by traditional Bayesian optimization (BO) methods. To optimize such functions, we propose a new method that…