Related papers: Refined Schur Method for Robust Pole Assignment wi…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
Elucidating the reasoning process with structured explanations from question to answer is crucial, as it significantly enhances the interpretability, traceability, and trustworthiness of question-answering (QA) systems. However, structured…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
Structured statistical estimation problems are often solved by Conditional Gradient (CG) type methods to avoid the computationally expensive projection operation. However, the existing CG type methods are not robust to data corruption. To…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
Pole-swapping algorithms are generalizations of bulge-chasing algorithms for the generalized eigenvalue problem. Structure-preserving pole-swapping algorithms for the palindromic and alternating eigenvalue problems, which arise in control…
We consider the uniqueness of solution (i.e., nonsingularity) of systems of $r$ generalized Sylvester and $\star$-Sylvester equations with $n\times n$ coefficients. After several reductions, we show that it is sufficient to analyze periodic…
We investigate global solutions to the Euler-alignment system in $d$ dimensions with unidirectional flows and strongly singular communication protocols $\phi(x) = |x|^{-(d+\alpha)}$ for $\alpha \in (0,2)$. Our paper establishes global…
Pole-swapping algorithms, which are generalizations of the QZ algorithm for the generalized eigenvalue problem, are studied. A new modular (and therefore more flexible) convergence theory that applies to all pole-swapping algorithms is…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
A greedy randomized augmented Kaczmarz (GRAK) method was proposed in [Z.-Z. Bai and W.-T. WU, SIAM J. Sci. Comput., 43 (2021), pp. A3892-A3911] for large and sparse inconsistent linear systems. However, one has to construct two new index…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
We construct a vertex model whose partition function is a refined dual Grothendieck polynomial, where the states are interpreted as nonintersecting lattice paths. Using this, we show refined dual Grothendieck polynomials are multi-Schur…
This paper presents a novel approach for solving the pole placement and eigenstructure assignment problems through data-driven methods. By using open-loop data alone, the paper shows that it is possible to characterize the allowable…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
This paper introduces a new method for constructing approximate solutions to a class of Wiener--Hopf equations. This is particularly useful since exact solutions of this class of Wiener--Hopf equations, at the moment, cannot be obtained.…
Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…
This paper studies the robustness of feature attribution methods for deep neural networks. It challenges the current notion of attributional robustness that largely ignores the difference in the model's outputs and introduces a new way of…
We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…