Related papers: Extremal Probability Bounds in Combinatorial Optim…
We consider maximization of stochastic monotone continuous submodular functions (CSF) with a diminishing return property. Existing algorithms only guarantee the performance \textit{in expectation}, and do not bound the probability of…
This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
In this paper, we obtain bounds on the probability of convergence to the optimal solution for the compact Genetic Algorithm (cGA) and the Population Based Incremental Learning (PBIL). We also give a sufficient condition for convergence of…
We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this…
We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors.…
We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…
Many upper bounds for the moduli of polynomial roots have been proposed but reportedly assessed on selected examples or restricted classes only. Regarding quality measured in terms of worst-case relative overestimation of the maximum…
We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…
We show that the problem of finding the measure supported on a compact subset K of the complex plane such that the variance of the least squares predictor by polynomials of degree at most n at a point exterior to K is a minimum, is…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
Let $f, f_1, \ldots, f_\nV$ be polynomials with rational coefficients in the indeterminates $\bfX=X_1, \ldots, X_n$ of maximum degree $D$ and $V$ be the set of common complex solutions of $\F=(f_1,\ldots, f_\nV)$. We give an algorithm…
Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These…
Causal queries are often only partially identifiable from observational data, and experiments that could tighten the resulting bounds are typically costly. We study the problem of selecting, prior to observing experimental outcomes, a…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…