A Linear Programming Inequality with Applications to Concentration of Measure

TL;DR

This paper introduces a simple linear programming inequality that bounds the maximum of certain programs, enabling new concentration of measure results for dependent variables and potentially serving as a useful tool in related fields.

Contribution

It presents a novel linear programming inequality that generalizes existing concentration bounds to dependent random variables, with potential independent interest.

Findings

Bound on the maximal value of specific linear programs

Generalization of concentration inequalities for dependent variables

Potential applications in probability and optimization

Abstract

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some recent concentration of measure results. The linear programming inequality may be of independent interest.