Related papers: The quasi-optimality criterion in the linear funct…

This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing…

Nonlinear control systems with partial information to the decision maker are prevalent in a variety of applications. As a step toward studying such nonlinear systems, this work explores reinforcement learning methods for finding the optimal…

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…

The success of nonlinear noise reduction applied to a single channel recording of human voice is measured in terms of the recognition rate of a commercial speech recognition program in comparison to the optimal linear filter. The overall…

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…

This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random…

This paper considers the linear-quadratic dual control problem where the system parameters need to be identified and the control objective needs to be optimized in the meantime. Contrary to existing works on data-driven linear-quadratic…

We study Neural Optimal Transport in infinite-dimensional Hilbert spaces. In non-regular settings, Semi-dual Neural OT often generates spurious solutions that fail to accurately capture target distributions. We analytically characterize…

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Neuromorphic neural network processors, in the form of compute-in-memory crossbar arrays of memristors, or in the form of subthreshold analog and mixed-signal ASICs, promise enormous advantages in compute density and energy efficiency for…

In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, "$N$-convex functionals" (the simplest example being the maximum of several fractional-linear functions) of unknown "signal"…

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…

This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…

This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…

This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…

Given a set of human's decisions that are observed, inverse optimization has been developed and utilized to infer the underlying decision making problem. The majority of existing studies assumes that the decision making problem is with a…

Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…