相关论文: New rigorous perturbation bounds for the LU and QR…

Neural Lyapunov and barrier certificates have recently been used as powerful tools for verifying the safety and stability properties of deep reinforcement learning (RL) controllers. However, existing methods offer guarantees only under…

A new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a…

We provide a general framework for handling the effects of a unitary disturbance on the estimation of the amplitude $\lambda$ associated to a unitary dynamics. By computing an analytical and general expression for the quantum Fisher…

Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…

In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…

Building on the recent derivation of a bare factorization theorem for the $b$-quark induced contribution to the $h\to\gamma\gamma$ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization…

Anomalies are known to appear in the perturbation theory for the one-dimensional Anderson model. A systematic approach to anomalies at critical points of products of random matrices is developed, classifying and analysing their possible…

Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing…

This paper presents adaptive robust quadratic program (QP) based control using control Lyapunov and barrier functions for nonlinear systems subject to time-varying and state-dependent uncertainties. An adaptive estimation law is proposed to…

The perturbative instability of NLO collinear factorisation (CF) computations of $p_T$-integrated cross sections of heavy quarkonium production at high hadronic or photon-hadron collision energy is discussed. We resolve this problem via the…

There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given…

This paper deals with the analysis of a recent reformulation of the primal-dual hybrid gradient method [Zhu and Chan 2008, Pock, Cremers, Bischof and Chambolle 2009, Esser, Zhang and Chan 2010, Chambolle and Pock 2011], which allows to…

We perturb a real matrix $A$ of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions,…

Based on a factorization of an input covariance matrix, we define a mild generalization of an upper bound of Nikolov (2015) and Li and Xie (2020) for the NP-Hard constrained maximum-entropy sampling problem (CMESP). We demonstrate that this…

We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in perturbative QCD. We evaluate the master…

Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making. While such bounds…

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…

We postulate a supplemental power counting within the heavy quark effective theory, that results in a small, highly-constrained set of second-order power corrections, compared to the standard approach. We determine all $\bar{B} \to D^{(*)}$…