# Improved Gradient-Based Optimization Over Discrete Distributions

arXiv: https://arxiv.org/abs/1810.00116 · HTML: https://mlsanity.com/paper/1810.00116/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2018.

## Built on by (most cited first, 3 of 3)

- [Quantum-Aided Meta-Learning for Bayesian Binary Neural Networks via Born Machines](https://mlsanity.com/paper/2203.17089/) (2022)
- [Revisiting the Gumbel-Softmax in MADDPG](https://mlsanity.com/paper/2302.11793/) (2023)
- [What to Do When Your Discrete Optimization Is the Size of a Neural Network?](https://mlsanity.com/paper/2402.10339/) (2024)

## Abstract (arXiv)

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze existing solutions including finite-difference (FD) estimators and continuous relaxation (CR) estimators in terms of bias and variance. We show that the commonly used Gumbel-Softmax estimator is biased and propose a simple method to reduce it. We also derive a simpler piece-wise linear continuous relaxation that also possesses reduced bias. We demonstrate empirically that reduced bias leads to a better performance in variational inference and on binary optimization tasks.