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We present a methodology for bounding the error term of an asymptotic solution to a singularly perturbed optimal control (SPOC) problem whose exact solution is known to be computationally intractable. In previous works, reduced or…
Data-driven stochastic optimization is ubiquitous in machine learning and operational decision-making problems. Sample average approximation (SAA) and model-based approaches such as estimate-then-optimize (ETO) or integrated…
This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured…
In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety…
Stochastic difference-of-convex (DC) optimization is prevalent in numerous machine learning applications, yet its convergence properties under small batch sizes remain poorly understood. Existing methods typically require large batches or…
Consensus-based optimization (CBO) is a multi-agent metaheuristic derivative-free optimization algorithm that has proven to be capable of globally minimizing nonconvex nonsmooth functions across a diverse range of applications while being…
Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
A discrete time stochastic feedback control system with a noisy communication channel between the sensor and the controller is considered. The sensor has limited memory. At each time, the sensor transmits encoded symbol over the channel and…
Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
We consider sequences-indexed by time (discrete stages)-of families of multistage stochastic optimization problems. At each time, the optimization problems in a family are parameterized by some quantities (initial states, constraint…
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
Sharpness-Aware Minimization (SAM) is an optimizer that takes a descent step based on the gradient at a perturbation $y_t = x_t + \rho \frac{\nabla f(x_t)}{\lVert \nabla f(x_t) \rVert}$ of the current point $x_t$. Existing studies prove…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…