### 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 Subgradient 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.

Original language | English (US) |
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Pages (from-to) | 7125-7135 |

Number of pages | 11 |

Journal | Advances in Neural Information Processing Systems |

Volume | 2018-December |

State | Published - Jan 1 2018 |

Externally published | Yes |

Event | 32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: Dec 2 2018 → Dec 8 2018 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Information Systems
- Signal Processing

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## Cite this

*Advances in Neural Information Processing Systems*,

*2018-December*, 7125-7135.