CARMS: Categorical-Antithetic-REINFORCE Multi-Sample Gradient Estimator

TL;DR

CARMS introduces an unbiased, variance-reducing gradient estimator for categorical variables using antithetic sampling and copula-based methods, improving training of discrete models across various tasks.

Contribution

The paper presents CARMS, a novel multi-sample gradient estimator for categorical variables that combines REINFORCE with copula-based antithetic sampling, generalizing previous estimators and reducing variance.

Findings

CARMS outperforms existing methods on benchmark generative tasks.

It achieves lower variance in gradient estimates.

The method is effective across multiple discrete modeling tasks.

Abstract

Accurately backpropagating the gradient through categorical variables is a challenging task that arises in various domains, such as training discrete latent variable models. To this end, we propose CARMS, an unbiased estimator for categorical random variables based on multiple mutually negatively correlated (jointly antithetic) samples. CARMS combines REINFORCE with copula based sampling to avoid duplicate samples and reduce its variance, while keeping the estimator unbiased using importance sampling. It generalizes both the ARMS antithetic estimator for binary variables, which is CARMS for two categories, as well as LOORF/VarGrad, the leave-one-out REINFORCE estimator, which is CARMS with independent samples. We evaluate CARMS on several benchmark datasets on a generative modeling task, as well as a structured output prediction task, and find it to outperform competing methods including a strong self-control baseline. The code is publicly available.