Related papers: Stochastic Vs Worst-case Condition Numbers

Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an end-to-end view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own.…

In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded…

We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an…

Recent research has introduced a key notion of $H$-consistency bounds for surrogate losses. These bounds offer finite-sample guarantees, quantifying the relationship between the zero-one estimation error (or other target loss) and the…

We find that, in a linear model, the James-Stein estimator, which dominates the maximum-likelihood estimator in terms of its in-sample prediction error, can perform poorly compared to the maximum-likelihood estimator in out-of-sample…

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…

Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to study the case of a multiobjective optimization problem…

We study algorithms for computing stable models of propositional logic programs and derive estimates on their worst-case performance that are asymptotically better than the trivial bound of O(m 2^n), where m is the size of an input program…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…

Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic…

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said…

Stochastic encoders have been used in rate-distortion theory and neural compression because they can be easier to handle. However, in performance comparisons with deterministic encoders they often do worse, suggesting that noise in the…

In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the…

We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…

This paper concerns quantitative analysis of errors generated by incompletely known data in convex minimization problems. The problems are discussed in the mixed setting and the duality gap is used as the fundamental error measure. The…

In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input. This approach has countless success stories, but there are also important computational problems --- like…

The super-twisting differentiator, also known as the first-order robust exact differentiator, is a well known sliding mode differentiator. In the absence of measurement noise, it achieves exact reconstruction of the time derivative of a…

We perform a smoothed analysis of the componentwise condition numbers for determinant computation, matrix inversion, and linear equations solving for sparse n times n matrices. The bounds we obtain for the ex- pectations of the logarithm of…

Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of instantaneous SNRs of fading channels as a…