17 research outputs found
DiCE: The Infinitely Differentiable Monte-Carlo Estimator
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
DiCE: The Infinitely Differentiable Monte-Carlo Estimator
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
Efficient Sketching Algorithm for Sparse Binary Data
Recent advancement of the WWW, IOT, social network, e-commerce, etc. have
generated a large volume of data. These datasets are mostly represented by high
dimensional and sparse datasets. Many fundamental subroutines of common data
analytic tasks such as clustering, classification, ranking, nearest neighbour
search, etc. scale poorly with the dimension of the dataset. In this work, we
address this problem and propose a sketching (alternatively, dimensionality
reduction) algorithm -- \binsketch (Binary Data Sketch) -- for sparse binary
datasets. \binsketch preserves the binary version of the dataset after
sketching and maintains estimates for multiple similarity measures such as
Jaccard, Cosine, Inner-Product similarities, and Hamming distance, on the same
sketch. We present a theoretical analysis of our algorithm and complement it
with extensive experimentation on several real-world datasets. We compare the
performance of our algorithm with the state-of-the-art algorithms on the task
of mean-square-error and ranking. Our proposed algorithm offers a comparable
accuracy while suggesting a significant speedup in the dimensionality reduction
time, with respect to the other candidate algorithms. Our proposal is simple,
easy to implement, and therefore can be adopted in practice