Learning from Satisfying Assignments Using Risk Minimization

TL;DR

This paper addresses learning distributions over satisfying assignments of Boolean functions by applying risk minimization techniques, extending previous work on uniform and known distribution cases.

Contribution

It introduces a new approach using standard optimization algorithms for risk minimization to estimate distributions over satisfying assignments.

Findings

Proves theoretical guarantees for the proposed risk minimization approach.

Extends previous models to more general distribution estimation scenarios.

Provides analysis based on parameter estimation techniques in statistical machine learning.

Abstract

In this paper we consider the problem of Learning from Satisfying Assignments introduced by \cite{1} of finding a distribution that is a close approximation to the uniform distribution over the satisfying assignments of a low complexity Boolean function $f$. In a later work \cite{2} consider the same problem but with the knowledge of some continuous distribution $D$ and the objective being to estimate $D_f$, which is $D$ restricted to the satisfying assignments of an unknown Boolean function $f$. We consider these problems from the point of view of parameter estimation techniques in statistical machine learning and prove similar results that are based on standard optimization algorithms for Risk Minimization.