Related papers: Optimistic optimization of a Brownian
We consider some random series parametrised by complex binary strings. The simplest case is that of Rademacher series, independent of a time parameter. This is then extended to the case of Fourier series on the circle with Rademacher…
In this paper we derive novel change of variable formulas for stochastic integrals w.r.t. a time-changed Brownian motion where we assume that the time-change is a general increasing stochastic process with finitely many jumps in a bounded…
A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…
In this article, we propose and develop a novel Bayesian algorithm for optimization of functions whose first and second partial derivatives are known. The basic premise is the Gaussian process representation of the function which induces a…
We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
Identifying optimal strategies for efficient spatial exploration is crucial, both for animals seeking food and for robotic search processes, where maximizing the covered area is a fundamental requirement. Here, we propose position resetting…
A new formula for the probability that a standard Brownian motion stays between two linear boundaries is proved. A simple algorithm is deduced. Uniform precision estimates are computed. Different implementations have been made available…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
Accelerator physics relies on numerical algorithms to solve optimization problems in online accelerator control and tasks such as experimental design and model calibration in simulations. The effectiveness of optimization algorithms in…
This paper proposes a new family of algorithms for the online optimisation of composite objectives. The algorithms can be interpreted as the combination of the exponentiated gradient and $p$-norm algorithm. Combined with algorithmic ideas…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
We study the extremes of variable speed branching Brownian motion (BBM) where the time-dependent "speed functions", which describe the time-inhomogeneous variance, converge to the identity function. We consider general speed functions lying…
We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach…
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…
Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
Consider a d-dimensional Brownian motion in a random potential defined by attaching a nonnegative and polynomially decaying potential around Poisson points. We introduce a repulsive interaction between the Brownian path and the Poisson…
We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We…