Automatic Differentiation of Programs with Discrete Randomness. Arya, G., Schauer, M., Schäfer, F., & Rackauckas, C. January, 2023. arXiv:2210.08572 [cs, math]![Automatic Differentiation of Programs with Discrete Randomness [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability $p$ of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters ($p$) is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our code package is available at https://github.com/gaurav-arya/StochasticAD.jl.
@misc{arya2023,
title = {Automatic {Differentiation} of {Programs} with {Discrete} {Randomness}},
url = {http://arxiv.org/abs/2210.08572},
doi = {10.48550/arXiv.2210.08572},
abstract = {Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability \$p\$ of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters (\$p\$) is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our code package is available at https://github.com/gaurav-arya/StochasticAD.jl.},
urldate = {2023-08-24},
publisher = {arXiv},
author = {Arya, Gaurav and Schauer, Moritz and Schäfer, Frank and Rackauckas, Chris},
month = jan,
year = {2023},
note = {arXiv:2210.08572 [cs, math]},
keywords = {Computer Science - Machine Learning, Mathematics - Numerical Analysis, Computer Science - Mathematical Software, Mathematics - Probability, neuroblox: fancy Julia methods},
annote = {Comment: In Proceedings of NeurIPS 2022},
file = {arXiv Fulltext PDF:/Users/lcneuro/Zotero/storage/3FDE4SZY/Arya et al. - 2023 - Automatic Differentiation of Programs with Discret.pdf:application/pdf},
}
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