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Lukas (author of prv accountant, wulu473) said that  `In general, adding any additional points is safe and won't affect the robustness negatively.`\n\nThe cause of these errors seems to be the grid for computing the  `mean()` function of the `PrivacyRandomVariableTruncated` class. The grid (`points` variable) used to compute the mean is constant apart from the lowest (`self.t_min`) and highest point (`self.t_max`).\n\nThis PR determines the grid (`points` variable)  based on the lowest and highest point. More information is below.\n\nBest\n\n**Observation**\n\nI debugged the code and arrived at some point at the `mean()` function of the `PrivacyRandomVariableTruncated` class. The grid (`points` variable) used to compute the mean is constant apart from the lowest (`self.t_min`) and highest point (`self.t_max`). See the line of code [here](https://github.com/microsoft/prv_accountant/blob/a95c4e2d41ff4886c3e4a84925edf878a6540e0a/prv_accountant/privacy_random_variables/abstract_privacy_random_variable.py#L52). It looks like this `[self.tmin, -0.1, -0.01, -0.001, -0.0001, -1e-05, 1e-05, 0.0001, 0.001, 0.01, 0.1, self.tmax]`.\n\nIt seems that the `tmin` and `tmax` are of the order of `[-12,12]` for the examples that I posted above and even up to `[-48,48]` for the example that jeandut posted in the https://github.com/pytorch/opacus/issues/604 issue whereas they are more like `[-7,7]` for the [readme example for DP-SGD](https://github.com/microsoft/prv_accountant#dp-sgd).\n\nWe suspect that the integration breaks down when the gridspacing between between `tmin` / `tmax` get's too large.\n\n**Proposed solution**\n\nDetermine the points grid based on `tmin` and `tmax`  but determines the start and end of the logspace based on `tmin` and `tmax`.\n\nBefore: (https://github.com/pytorch/opacus/blob/95df0904ae5d2b3aaa26b708e5067e9271624036/opacus/accountants/analysis/prv/prvs.py#L99-L106)\n\nAfter:\n```\n# determine points based on t_min and t_max\nlower_exponent = int(np.log10(np.abs(self.t_min)))\nupper_exponent = int(np.log10(self.t_max))\npoints = np.concatenate(\n    [\n        [self.t_min],\n        -np.logspace(start=lower_exponent, stop=-5, num=10),\n        [0],\n        np.logspace(start=-5, stop=upper_exponent, num=10),\n        [self.t_max],\n    ]\n)\n```\n\n## How Has This Been Tested (if it applies)\n\nI ran the examples from the issues https://github.com/pytorch/opacus/issues/601 and https://github.com/pytorch/opacus/issues/604 and they don't break anymore.\n\n```\nimport opacus\ntarget_delta = 0.001\ntarget_epsilon = 20\nsteps = 5000\nsample_rate=0.19120458891013384\n\nfor target_epsilon in [20, 50]:\n    noise_multiplier = opacus.privacy_engine.get_noise_multiplier(target_delta=target_delta, target_epsilon=target_epsilon, steps=steps, sample_rate=sample_rate, accountant=\"prv\")\n    prv_accountant = opacus.accountants.utils.create_accountant(\"prv\")\n    prv_accountant.history = [(noise_multiplier, sample_rate, steps)]\n    obtained_epsilon = prv_accountant.get_epsilon(delta=target_delta)\n    print(f\"target epsilon {target_epsilon}, obtained epsilon {obtained_epsilon}\")\n\n```\n> target epsilon 20, obtained epsilon 19.999332284974717\ntarget epsilon 50, obtained epsilon 49.99460075990896\n\n```\ntarget_epsilon = 4\nbatch_size = 50\nepochs = 5\ndelta = 1e-05\nexpected_len_dataloader = 500 // batch_size\nsample_rate = 1/expected_len_dataloader\n\nnoise_multiplier = opacus.privacy_engine.get_noise_multiplier(target_delta=target_delta, target_epsilon=target_epsilon, epochs=epochs, sample_rate=sample_rate, accountant=\"prv\")\nprv_accountant = opacus.accountants.utils.create_accountant(\"prv\")\nprv_accountant.history = [(noise_multiplier, sample_rate, int(epochs / sample_rate))]\nobtained_epsilon = prv_accountant.get_epsilon(delta=target_delta)\nprint(f\"target epsilon {target_epsilon}, obtained epsilon {obtained_epsilon}\")\n\n```\n> target epsilon 4, obtained epsilon 3.9968389923130356\n\n## Checklist\n\n- [x] The documentation is up-to-date with the changes I made.\n- [x] I have read the **CONTRIBUTING** document and completed the CLA (see **CONTRIBUTING**).\n- [ ] All tests passed, and additional code has been covered with new tests.\n\nNot able to run all tests locally and unsure if new tests should be added.\n\nPull Request resolved: https://github.com/pytorch/opacus/pull/606\n\nReviewed By: HuanyuZhang\n\nDifferential Revision: D50111887\n\nfbshipit-source-id: 2f77f8bc0e59837f765b87f2e107bc01015b9481","shortMessageHtmlLink":"fix: make prv accountant robust to larger epsilons (<a class=\"issue-link js-issue-link\" data-error-text=\"Failed to load title\" data-id=\"1934376871\" data-permission-text=\"Title is private\" data-url=\"https://github.com/pytorch/opacus/issues/606\" data-hovercard-type=\"pull_request\" data-hovercard-url=\"/pytorch/opacus/pull/606/hovercard\" href=\"https://github.com/pytorch/opacus/pull/606\">#606</a>)"}},{"before":"8dfdc2ed9af7ff4aa64cab65c4831233468fe988","after":"3d622d0d4bafed63ab1cc2bdc6f8a88f26ab0089","ref":"refs/heads/main","pushedAt":"2023-11-09T21:00:39.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"facebook-github-bot","name":"Facebook Community Bot","path":"/facebook-github-bot","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/6422482?s=80&v=4"},"commit":{"message":"Fix the import order for D51126461 (#610)\n\nSummary:\nPull Request resolved: https://github.com/pytorch/opacus/pull/610\n\nIn D51126461, we did not import the library according to the alphabetical order, therefore triggering some linter test failure. 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