[New accountant] Numerical composition #378
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Summary: This PR implements a new accountant `PRVAccountant` based on the paper [Numerical Composition of Differential Privacy](https://arxiv.org/abs/2106.02848). Code inspired heavily by the code that accompanied the paper: https://github.com/microsoft/prv_accountant ## Types of changes - [ ] Bug fix (non-breaking change which fixes an issue) - [x] New feature (non-breaking change which adds functionality) - [ ] Breaking change (fix or feature that would cause existing functionality to change) - [ ] Docs change / refactoring / dependency upgrade ## Motivation and Context / Related issue See #378 ## How Has This Been Tested (if it applies) I have tested these changes with the following scripts, but would welcome suggestions on how to test further or write unit tests to cover these changes: - [validate_gaussian.py](https://gist.github.com/tcbegley/13483859eb07488d711368c982af5ded) recreates [this notebook](https://github.com/microsoft/prv_accountant/blob/main/notebooks/validate-gaussian.ipynb), which checks that we can recover upper and lower bounds on the privacy curve of a Gaussian mechanism correctly. - [prv_accountant_cifar10.py](https://gist.github.com/tcbegley/91afccc8f702a61617f7ec6da250effe) runs [this tutorial from the Opacus docs](https://opacus.ai/tutorials/building_image_classifier) with the `PRVAccountant` instead of `RDPAccountant`. ## Checklist I have not yet written docstrings or tests for these changes both as it was slightly unclear to me how best to proceed, but also because I would like to validate the approach taken in this initial implementation before polishing. - [x] The documentation is up-to-date with the changes I made. - [x] I have read the **CONTRIBUTING** document and completed the CLA (see **CONTRIBUTING**). - [x] All tests passed, and additional code has been covered with new tests. Pull Request resolved: #493 Reviewed By: ffuuugor Differential Revision: D39208724 Pulled By: alexandresablayrolles fbshipit-source-id: c8949c2a61a0a6ed24628a5f53e597f2108a5b91
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https://arxiv.org/abs/2106.02848
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