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In practice, optimization models are often prone to unavoidable inaccuracies due to dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on…
In this paper, infinite horizon stochastic difference equations and backward stochastic difference equations with fractional noises are studied. The main difficulty comes from fractional noises on infinite horizon. Motivated by…
PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
This paper studies the optimal control problems of stochastic evolution equations with infinite delay of general functional type. By introducing a non-anticipative path derivative and its infinite-window dual operator, we derive the…
We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization…
In this paper, we consider the stochastic optimal control problems under model risk caused by uncertain volatilities. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brwonian motion…
Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as…
Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…
Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global optima often faces NP-hardness, and thus only locally optimal…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system…
This paper presents a robust and kernelized data-enabled predictive control (RoKDeePC) algorithm to perform model-free optimal control for nonlinear systems using only input and output data. The algorithm combines robust predictive control…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
We investigate the distribution and multiple occurrences of extreme events stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on $\mathbb{R}^n$. We do so by studying the action of an annealead…
There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics…
In this paper, we consider optimal control problems of stochastic Volterra equations (SVEs) with singular kernels, where the control domain is not necessarily convex. We establish a global maximum principle by means of the spike variation…