Low-variance Black-box Gradient Estimates for the Plackett-Luce Distribution

This repo contains code for our paper Low-variance Black-box Gradient Estimates for the Plackett-Luce Distribution.

Abstract

Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradients. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. In particular, the control variates allow us to optimize black-box functions over permutations using stochastic gradient descent. To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data. We show that for differentiable functions, our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.

Citation

@inproceedings{gadetsky2020lowvariance,
  author    = {Artyom Gadetsky and
               Kirill Struminsky and
               Christopher Robinson and
               Novi Quadrianto and
               Dmitry P. Vetrov},
  title     = {Low-Variance Black-Box Gradient Estimates for the Plackett-Luce Distribution},
  booktitle = {The Thirty-Fourth {AAAI} Conference on Artificial Intelligence, {AAAI}
               2020, New York, NY, USA, February 7-12, 2020},
  pages     = {10126--10135},
  publisher = {{AAAI} Press},
  year      = {2020},
  url       = {https://aaai.org/ojs/index.php/AAAI/article/view/6572}
}

Toy Experiment

Prepare environment (maybe you'll need to change cudatoolkit version in toy_env.yml or even use cpuonly version of PyTorch):

conda env create -f toy_env.yml
conda activate toy_env

Run toy_experiment.py:

python toy_experiment.py --estimator exact
python toy_experiment.py --estimator reinforce
python toy_experiment.py --estimator rebar
python toy_experiment.py --estimator relax

Plot figure using plot_toy.ipynb

Results were obtained using cpu. Quantitative results for cuda may vary slighlty due to randomness in cuda kernels, but qualitative results remain the same.