Probabilistic Tools for the Analysis of Randomized Optimization Heuristics

TL;DR

This chapter compiles various probabilistic tools, including classic inequalities and advanced concepts, to aid in analyzing randomized search heuristics and other randomized algorithms.

Contribution

It provides a comprehensive collection of probabilistic methods, including lesser-known tools, for analyzing randomized heuristics and algorithms.

Findings

Includes Markov, Chebyshev, and Chernoff inequalities.

Introduces stochastic domination and coupling techniques.

Presents Chernoff bounds for specialized distributions.

Abstract

This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like stochastic domination and coupling or Chernoff bounds for geometrically distributed random variables and for negatively correlated random variables. Most of the results presented here have appeared previously, some, however, only in recent conference publications. While the focus is on collecting tools for the analysis of randomized search heuristics, many of these may be useful as well in the analysis of classic randomized algorithms or discrete random structures.