相关论文: Sensitivity Analysis of Stochastic Constraint and …
In this article a stochastic particle system approximation to the parametric sensitivity in the Smoluchowski coagulation equation is introduced. The parametric sensitivity is the derivative of the solution to the equation with respect to…
In this paper, we propose a novel robust stochastic optimization approach with a distinctive consideration for rare events, in which divergence measures are used to bound the event-wise ambiguity sets. This is done by using the Poisson…
This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In particular, we establish smoothness results for the optimal…
In decision-dependent games, multiple players optimize their decisions under a data distribution that shifts with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics…
This article presents a general multivariate $f$-sensitivity index, rooted in the $f$-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the…
We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…
In this paper, sensitivity analysis of the efficient sets in parametric convex vector optimization is considered. Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps. We establish the…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $\Sigma$ and a stochastic memoryless map $\Psi$. After that, we extend the result to the class of large…
We present a new methodology for computing sensitivities in evolutionary systems using a model-driven low-rank approximation. To this end, we formulate a variational principle that seeks to minimize the distance between the time derivative…
This paper concerns applications of variational analysis to some local aspects of behavioral science modeling by developing an effective variational rationality approach to these and related issues. Our main attention is paid to local…
Stochastic policies (also known as relaxed controls) are widely used in continuous-time reinforcement learning algorithms. However, executing a stochastic policy and evaluating its performance in a continuous-time environment remain open…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a…
In Part 1 of this paper, we have estimated the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
We describe a design principle for adaptive systems under which adaptation is driven by particular challenges that the environment poses, as opposed to average or otherwise aggregated measures of performance over many challenges. We trace…
Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…
We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…