Related papers: Adaptive Approximation of the Minimum of Brownian …
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
We address the problem of optimizing a Brownian motion. We consider a (random) realization $W$ of a Brownian motion with input space in $[0,1]$. Given $W$, our goal is to return an $\epsilon$-approximation of its maximum using the smallest…
We study the approximation of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H>1/2$. For the mean-square error at a single point we derive the optimal rate of convergence that can be achieved…
We provide a simple algorithm for construction of Brownian paths approximating those of a L\'evy process on a finite time interval. It requires knowledge of the L\'evy process trajectory on a chosen regular grid and the law of its endpoint,…
We study the law of the minimum of a Brownian bridge, conditioned to take specific values at specific points, and the law of the location of the minimum. They are used to compare some non-adaptive optimisation algorithms for black-box…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…
In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the expansion of Brownian motion in this polynomial basis are…
We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but…
In this paper, we study the tradeoff between the approximation guarantee and adaptivity for the problem of maximizing a monotone submodular function subject to a cardinality constraint. The adaptivity of an algorithm is the number of…
We study the first-passage time, the distribution of the maximum, and the absorption probability of fractional Brownian motion of Hurst parameter $H$ with both a linear and a non-linear drift. The latter appears naturally when applying…
We present an algorithm to efficiently sample first-passage times for fractional Brownian motion. To increase the resolution, an initial coarse lattice is successively refined close to the target, by adding exactly sampled midpoints, where…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
The problem of detecting a change in the drift of a Brownian motion is considered. The change point is assumed to have a modified exponential prior distribution with unknown parameters. A worst-case analysis with respect to these parameters…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
Piecewise linearization is a key technique for solving nonlinear problems in transportation network design and other optimization fields, in which generating breakpoints is a fundamental task. This paper proposes an optimal breakpoint…
Considering the paradigmatic driven Brownian motion, we perform extensive numerical analysis on the performance of optimal linear-response processes far from equilibrium. We focus on the overdamped regime where exact optimal processes are…