Finding Probably Approximate Optimal Solutions by Training to Estimate the Optimal Values of Subproblems

TL;DR

This paper introduces a novel solver for binary optimization problems that estimates subproblem optimal values using a trained estimator, avoiding the need for solving instances directly.

Contribution

It proposes a new training approach for estimators based on an inequality, enabling approximate solutions without solving each instance.

Findings

The estimator effectively predicts optimal subproblem values.

The method reduces computational effort compared to traditional solvers.

It does not require solving instances during training.

Abstract

The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of objectives and their respective sub-instances. The training of the estimator is based on an inequality that facilitates the use of the expected total deviation from optimality conditions as a loss function rather than the objective-function itself. Thus, it does not calculate values of policies, nor does it rely on solved instances.