Related papers: Input-to-State Stability of Gradient Flows in Dist…
Domain generalization aims at learning a universal model that performs well on unseen target domains, incorporating knowledge from multiple source domains. In this research, we consider the scenario where different domain shifts occur among…
This study focuses on a Wasserstein-type gradient flow, which represents an optimization process of a continuous model of a Deep Neural Network (DNN). First, we establish the existence of a minimizer for an average loss of the model under…
We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over Banach spaces, time-delay systems, ordinary differential equations…
We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a…
In idealized models of a quantum register and its environment, quantum information can be stored indefinitely by encoding it into a decoherence-free subspace (DFS). Nevertheless, perturbations to the idealized register-environment coupling…
We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…
Recent studies revealed the mathematical connection of deep neural network (DNN) and dynamic system. However, the fundamental principle of DNN has not been fully characterized with dynamic system in terms of optimization and generalization.…
Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
Since the concept of input-to-state stability (ISS) was introduced, it has been extensively investigated for finite-dimensional control systems and has recently received attention for infinite-dimensional systems. While numerical techniques…
This paper investigates the asymptotic behavior of stochastic recursive inclusions in the presence of non-zero, non-diminishing bias, a setting that frequently arises in zeroth-order optimization, stochastic approximation with…
The aggressive integration of distributed renewable sources is changing the dynamics of the electric power grid in an unexpected manner. As a result, maintaining conventional performance specifications, such as transient stability, may not…
In this paper, we consider a class of denial-of-service (DoS) attacks, which aims at overloading the communication channel. On top of the security issue, continuous or periodic transmission of information within feedback loop is necessary…
Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially…
With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before…
We consider the distributionally robust optimization (DRO) model of principal component analysis (PCA) to account for uncertainty in the underlying probability distribution. The resulting formulation leads to a nonsmooth constrained min-max…
We propose a distributionally robust data-driven predictive control framework for stochastic linear time-invariant systems with unknown dynamics and disturbance distributions. We use an offline trajectory to fit the subspace predictive…
The generalized hydrodynamic (GHD) approach has been extremely successful in describing the out-of-equilibrium properties of a great variety of integrable many-body quantum systems. It naturally extracts the large-scale dynamical degrees of…