The score function estimator is widely used for estimating gradients of
stochastic objectives in Stochastic Computation Graphs (SCG), eg. in
reinforcement learning and meta-learning. While deriving the first-order
gradient estimators by differentiating a surrogate loss (SL) objective is
computationally and conceptually simple, using the same approach for
higher-order gradients is more challenging. Firstly, analytically deriving and
implementing such estimators is laborious and not compliant with automatic
differentiation. Secondly, repeatedly applying SL to construct new objectives
for each order gradient involves increasingly cumbersome graph manipulations.
Lastly, to match the first-order gradient under differentiation, SL treats part
of the cost as a fixed sample, which we show leads to missing and wrong terms
for higher-order gradient estimators. To address all these shortcomings in a
unified way, we introduce DiCE, which provides a single objective that can be
differentiated repeatedly, generating correct gradient estimators of any order
in SCGs. Unlike SL, DiCE relies on automatic differentiation for performing the
requisite graph manipulations. We verify the correctness of DiCE both through a
proof and through numerical evaluation of the DiCE gradient estimates. We also
use DiCE to propose and evaluate a novel approach for multi-agent learning. Our
code is available at https://goo.gl/xkkGxN.
Описание
[1802.05098] DiCE: The Infinitely Differentiable Monte-Carlo Estimator
%0 Generic
%1 foerster2018infinitely
%A Foerster, Jakob
%A Farquhar, Greg
%A Al-Shedivat, Maruan
%A Rocktäschel, Tim
%A Xing, Eric P.
%A Whiteson, Shimon
%D 2018
%K 2018 machine-learning
%T DiCE: The Infinitely Differentiable Monte-Carlo Estimator
%U http://arxiv.org/abs/1802.05098
%X The score function estimator is widely used for estimating gradients of
stochastic objectives in Stochastic Computation Graphs (SCG), eg. in
reinforcement learning and meta-learning. While deriving the first-order
gradient estimators by differentiating a surrogate loss (SL) objective is
computationally and conceptually simple, using the same approach for
higher-order gradients is more challenging. Firstly, analytically deriving and
implementing such estimators is laborious and not compliant with automatic
differentiation. Secondly, repeatedly applying SL to construct new objectives
for each order gradient involves increasingly cumbersome graph manipulations.
Lastly, to match the first-order gradient under differentiation, SL treats part
of the cost as a fixed sample, which we show leads to missing and wrong terms
for higher-order gradient estimators. To address all these shortcomings in a
unified way, we introduce DiCE, which provides a single objective that can be
differentiated repeatedly, generating correct gradient estimators of any order
in SCGs. Unlike SL, DiCE relies on automatic differentiation for performing the
requisite graph manipulations. We verify the correctness of DiCE both through a
proof and through numerical evaluation of the DiCE gradient estimates. We also
use DiCE to propose and evaluate a novel approach for multi-agent learning. Our
code is available at https://goo.gl/xkkGxN.
@misc{foerster2018infinitely,
abstract = {The score function estimator is widely used for estimating gradients of
stochastic objectives in Stochastic Computation Graphs (SCG), eg. in
reinforcement learning and meta-learning. While deriving the first-order
gradient estimators by differentiating a surrogate loss (SL) objective is
computationally and conceptually simple, using the same approach for
higher-order gradients is more challenging. Firstly, analytically deriving and
implementing such estimators is laborious and not compliant with automatic
differentiation. Secondly, repeatedly applying SL to construct new objectives
for each order gradient involves increasingly cumbersome graph manipulations.
Lastly, to match the first-order gradient under differentiation, SL treats part
of the cost as a fixed sample, which we show leads to missing and wrong terms
for higher-order gradient estimators. To address all these shortcomings in a
unified way, we introduce DiCE, which provides a single objective that can be
differentiated repeatedly, generating correct gradient estimators of any order
in SCGs. Unlike SL, DiCE relies on automatic differentiation for performing the
requisite graph manipulations. We verify the correctness of DiCE both through a
proof and through numerical evaluation of the DiCE gradient estimates. We also
use DiCE to propose and evaluate a novel approach for multi-agent learning. Our
code is available at https://goo.gl/xkkGxN.},
added-at = {2018-02-16T13:48:25.000+0100},
author = {Foerster, Jakob and Farquhar, Greg and Al-Shedivat, Maruan and Rocktäschel, Tim and Xing, Eric P. and Whiteson, Shimon},
biburl = {https://www.bibsonomy.org/bibtex/281d1c63dc664344e7417bac897beec2b/achakraborty},
description = {[1802.05098] DiCE: The Infinitely Differentiable Monte-Carlo Estimator},
interhash = {30bd00fc76e1a27b35d77ac8b3bf0a59},
intrahash = {81d1c63dc664344e7417bac897beec2b},
keywords = {2018 machine-learning},
note = {cite arxiv:1802.05098},
timestamp = {2018-02-16T13:48:25.000+0100},
title = {DiCE: The Infinitely Differentiable Monte-Carlo Estimator},
url = {http://arxiv.org/abs/1802.05098},
year = 2018
}