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Unbiased Single-Queried Gradient for Combinatorial Objective

Year: 2026
Type: preprint
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.
Open Access status: green
OpenAlex ID: W7127912191
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