Related papers: Optimistic optimization of a Brownian
In this paper, we consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in [10.11], we can investigate the…
We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can…
Let $B=\{ B_{t}\} _{t\ge 0}$ be a one-dimensional standard Brownian motion. As an application of a recent result of ours on exponential functionals of Brownian motion, we show in this paper that, for every fixed $t>0$, the process given by…
We study a family of potential functions for online learning. We show that if the potential function has strictly positive derivatives of order 1-4 then the min-max optimal strategy for the adversary is Brownian motion. Using that fact we…
Brown-Resnick processes are max-stable processes that are associated to Gaussian processes. Their simulation is often based on the corresponding spectral representation which is not unique. We study to what extent simulation accuracy and…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
One of the first tasks we learn as children is to grasp objects based on our tactile perception. Incorporating such skill in robots will enable multiple applications, such as increasing flexibility in industrial processes or providing…
Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
We study the problem of when a Brownian motion in the unit ball has a positive probability of avoiding a countable collection of spherical obstacles. We give a necessary and sufficient integral condition for such a collection to be…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search…
We provide experimental evaluation of a number of known and new algorithms for approximate computation of Monroe's and Chamberlin-Courant's rules. Our experiments, conducted both on real-life preference-aggregation data and on synthetic…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…
An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When the initial displacement is large, the central moments of…
Trajectory optimization (TO) is one of the most powerful tools for generating feasible motions for humanoid robots. However, including uncertainties and stochasticity in the TO problem to generate robust motions can easily lead to an…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…