  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 derivatives 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 derivative 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 estimators of higher-order derivatives. To address all these shortcomings
in a unified way, we introduce DiCE, which provides a single objective that can
be differentiated repeatedly, generating correct estimators of derivatives 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 numerical evaluation of the DiCE derivative estimates.
We also use DiCE to propose and evaluate a novel approach for multi-agent
learning. Our code is available at https://www.github.com/alshedivat/lola.
