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Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
To deal with stochastic hybrid systems with general state-dependent switching, we propose an approximation method by a sequence of stochastic hybrid systems with piecewise constant type switching. The convergence rate in the Wasserstein…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…
The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in distributing and treat the data…
We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…
We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the…
In this work, multiplicative stochasticity is applied to the learning rate of stochastic optimization algorithms, giving rise to stochastic learning-rate schemes. In-expectation theoretical convergence results of Stochastic Gradient Descent…
We consider stochastic algorithms derived from methods for solving deterministic optimization problems, especially comparison-based algorithms derived from stochastic approximation algorithms with a constant step-size. We develop a…
We consider an input-to-response (ItR) system characterized by (1) parameterized input with a known probability distribution and (2) stochastic ItR function with heteroscedastic randomness. Our purpose is to efficiently quantify the extreme…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
In this paper, we consider the stochastic Langevin equation with additive noises, which possesses both conformal symplectic geometric structure and ergodicity. We propose a methodology of constructing high weak order conformal symplectic…
In any Markov chain Monte Carlo analysis, rapid convergence of the chain to its target probability distribution is of practical and theoretical importance. A chain that converges at a geometric rate is geometrically ergodic. In this paper,…