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Accurately backpropagating the gradient through categorical variables is achallenging task that arises in various domains, such as training discretelatent variable models. To this end, we propose CARMS, an unbiased estimatorfor categorical random variables based on multiple mutually negativelycorrelated (jointly antithetic) samples. CARMS combines REINFORCE with copulabased sampling to avoid duplicate samples and reduce its variance, whilekeeping the estimator unbiased using importance sampling. It generalizes boththe ARMS antithetic estimator for binary variables, which is CARMS for twocategories, as well as LOORF/VarGrad, the leave-one-out REINFORCE estimator,which is CARMS with independent samples. We evaluate CARMS on several benchmarkdatasets on a generative modeling task, as well as a structured outputprediction task, and find it to outperform competing methods including a strongself-control baseline. The code is publicly available.

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