Paper Info
Title
Provably Correct Automatic Subdifferentiation for Qualified Programs.
Abstract
The Cheap Gradient Principle [Griewank and Walther, 2008] - the computational cost of computing the gradient of a scalar-valued function is nearly the same (often within a factor of 5) as that of simply computing the function itself - is of central importance in optimization; it allows us to quickly obtain (high dimensional) gradients of scalar loss functions which are subsequently used in black box gradient-based optimization procedures. The current state of affairs is markedly different with regards to computing subderivatives: widely used ML libraries, including TensorFlow and PyTorch, do not correctly compute (generalized) subderivatives even on simple examples. This work considers the question: is there a Cheap Sub gradient Principle? Our main result shows that, under certain restrictions on our library of nonsmooth functions (standard in nonlinear programming), provably correct generalized subderivatives can be computed at a computational cost that is within a (dimension-free) factor of 6 of the cost of computing the scalar function itself.
Year
Venue
Keywords
2018
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 31 (NIPS 2018)
loss functions,computational cost,high dimensional,scalar function,nonlinear programming,scalar-valued function
DocType
Volume
ISSN
Conference
31
1049-5258
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Sham Kakade14365282.77
Lee, Jason D.271148.29