On Estimation and Optimization of Mean Values of Bounded Variables

TL;DR

This paper introduces a comprehensive method for probabilistic estimation and optimization of bounded variables, combining explicit formulas, reliability control, and gradient-based algorithms for improved accuracy and efficiency.

Contribution

It presents a novel approach that integrates absolute and relative error criteria with Chernoff-Hoeffding bounds for reliable probabilistic estimation and optimization.

Findings

Developed an explicit formula for reliability control.

Transformed probabilistic minimization into a gradient-amenable optimization problem.

Demonstrated effectiveness of the approach through computational experiments.

Abstract

In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed criterion of absolute and relative errors. By employing the Chernoff-Hoeffding bound and the concept of sampling, the minimization of a probabilistic function is transformed into an optimization problem amenable for gradient descendent algorithms.