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Nonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time. Learning the Koopman operator and its spectral decomposition from data is enabled…
We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudo-polynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…
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…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
We study reinforcement learning in stochastic path (SP) problems. The goal in these problems is to maximize the expected sum of rewards until the agent reaches a terminal state. We provide the first regret guarantees in this general problem…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
In this work, we study discrete-time Markov decision processes (MDPs) under constraints with Borel state and action spaces and where all the performance functions have the same form of the expected total reward (ETR) criterion over the…
This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for L\'evy-driven SDEs or their integrands for stochastic integrals. Main results are bordered…
Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…
This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…