相关论文: Concise Complexity Analyses for Trust-Region Metho…

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…

Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…

We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size…

Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…

We consider variants of a recently-developed Newton-CG algorithm for nonconvex problems \citep{royer2018newton} in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on…

In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…

Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, due to its excessively conservative nature, this method of incomplete verification often cannot achieve an…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…

In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic…

This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…

Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular…

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

We present an adaptive trust-region method for unconstrained optimization that allows inexact solutions to the trust-region subproblems. Our method is a simple variant of the classical trust-region method of \citet{sorensen1982newton}. The…

In order for reinforcement learning techniques to be useful in real-world decision making processes, they must be able to produce robust performance from limited data. Deep policy optimization methods have achieved impressive results on…

The trust-region problem, which minimizes a nonconvex quadratic function over a ball, is a key subproblem in trust-region methods for solving nonlinear optimization problems. It enjoys many attractive properties such as an exact…

We introduce two multifidelity trust-region methods based on the Magical Trust Region (MTR) framework. MTR augments the classical trust-region step with a secondary, informative direction. In our approaches, the secondary ``magical''…

Acquisition of training data for the standard semantic segmentation is expensive if requiring that each pixel is labeled. Yet, current methods significantly deteriorate in weakly supervised settings, e.g. where a fraction of pixels is…

In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a…

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…