Unbiased Single-Queried Gradient for Combinatorial Objective

TL;DR

This paper introduces an unbiased stochastic gradient method for combinatorial optimization that requires only a single query, improving efficiency over traditional multiple-query approaches.

Contribution

It proposes a novel single-query unbiased stochastic gradient estimator for combinatorial problems, unifying REINFORCE and new gradient classes.

Findings

Unbiased gradient estimator with a single query

Includes REINFORCE as a special case

Introduces new classes of stochastic gradients

Abstract

In a probabilistic reformulation of a combinatorial problem, we often face an optimization over a hypercube, which corresponds to the Bernoulli probability parameter for each binary variable in the primal problem. The combinatorial nature suggests that an exact gradient computation requires multiple queries. We propose a stochastic gradient that is unbiased and requires only a single query of the combinatorial function. This method encompasses a well-established REINFORCE (through an importance sampling), as well as including a class of new stochastic gradients.