Conservative search for target epsilon in get_noise_multiplier #348

alexandresablayrolles · 2022-02-04T13:10:43Z

Problem

@tholop noticed in #346 that get_noise_multiplier can overshoot the target epsilon when searching for highest possible noise multiplier. This is because of the binary search implementation.

Changes

Noise multiplier now verifies that the actual epsilon is lower than the target epsilon.
- Added test for this.
Bounds of the range of search for sigma, and precision can now be given as arguments to get_noise_multiplier.

Differential Revision: D34003401

facebook-github-bot · 2022-02-04T13:11:21Z

This pull request was exported from Phabricator. Differential Revision: D34003401

romovpa · 2022-02-04T15:39:18Z

opacus/accountants/utils.py

    while eps > target_epsilon:
-        sigma_max = 2 * sigma_max
-        accountant.steps = [(sigma_max, sample_rate, int(epochs / sample_rate))]
+        sigma_high = 2 * sigma_high
+        accountant.steps = [(sigma_high, sample_rate, steps)]
        eps = accountant.get_epsilon(delta=target_delta, **kwargs)
-        if sigma_max > MAX_SIGMA:
+        if sigma_high > sigma_max:
            raise ValueError("The privacy budget is too low.")


Here we try to automatically initialize sigma_high for the binary search. This behaviour is not consistent with the docstring: I can set a specific bound but it can change it anyway. Also, having both sigma_high and sigma_max is counter-intuitive and it takes knowing the whole algorithm to understand what is the difference.

Proposal

Leave only sigma_low, sigma_high in parameters. I would also rename to min/max to emphasize that the result will be bounded:

def get_noise_multiplier( ... sigma_min: float = 0.01, sigma_max: Optional[float] = None, )

If sigma_max is None, run this part to get the upper bound starting from sigma_max+1.

Leave MAX_SIGMA a global constant, maybe make it higher.

romovpa · 2022-02-04T15:39:54Z

opacus/accountants/utils.py

+    sigma_precision=0.01,
+    sigma_low=0.01,
+    sigma_high=10,
+    sigma_max=2000,


Add type definitions please

romovpa · 2022-02-04T15:41:31Z

opacus/accountants/utils.py

    accountant: str = "rdp",
+    sigma_precision=0.01,


Let's rename it to sigma_tolerance, which is the common word used in optimization (see scipy.bisect).

Isn't this precision too low? I mean we should make this value lower, closer to typical float precision. Btw, this higher/lower confusion is another reason to rename the argument to tolerance.

romovpa · 2022-02-04T15:45:14Z

opacus/accountants/utils.py

+    epochs: int = None,
+    steps: int = None,


If the argument can be None, it should have type Optional[int]

romovpa · 2022-02-04T15:48:12Z

opacus/accountants/utils.py


-    return sigma
+    return sigma_high


A possible corner case when sigma_high < sigma_low is not considered here.

romovpa · 2022-02-04T15:51:39Z

opacus/accountants/utils.py

+    while sigma_high - sigma_low > sigma_precision:
+        sigma = (sigma_low + sigma_high) / 2
+        accountant.steps = [(sigma, sample_rate, steps)]
        eps = accountant.get_epsilon(delta=target_delta, **kwargs)

        if eps < target_epsilon:
-            sigma_max = sigma
+            sigma_high = sigma
        else:
-            sigma_min = sigma
+            sigma_low = sigma


I'm thinking if we can use scipy.optimzie.bisect() instead of implementing our own.
It is easy to implement binary search incorrectly so we need to make tests for all corner cases. If we use scipy, we don't need to add our own tests, plus it is much more stable than the rest of our dependencies.

romovpa · 2022-02-04T15:53:16Z

opacus/accountants/utils.py

    accountant: str = "rdp",
+    sigma_precision=0.01,


You need to add check that sigma_tolerance is strictly positive. Alternative: pass is to scipy.bisect and let it do the check for you.

facebook-github-bot · 2022-02-10T13:01:16Z

This pull request was exported from Phabricator. Differential Revision: D34003401

Summary: Pull Request resolved: pytorch#348 Noise multiplier now verifies that the actual epsilon is *lower* than the target epsilon. Bounds of the range of search for sigma, and precision can now be given as arguments to get_noise_multiplier. Differential Revision: D34003401 fbshipit-source-id: bed5aab383a867d1608e692c54c0832b8acef373

Summary: Pull Request resolved: pytorch#348 Noise multiplier now verifies that the actual epsilon is *lower* than the target epsilon. Bounds of the range of search for sigma, and precision can now be given as arguments to get_noise_multiplier. Differential Revision: D34003401 fbshipit-source-id: ba00d6bc0a60bdba71564a81dd5e895590c7a0ea

facebook-github-bot · 2022-02-11T14:04:03Z

This pull request was exported from Phabricator. Differential Revision: D34003401

romovpa · 2022-02-11T17:23:20Z

opacus/accountants/utils.py

+    eps = accountant.get_epsilon(delta=target_delta, **kwargs)
+    if eps < target_epsilon:
+        warnings.warn(
+            f"Noise multiplier of {sigma_low} is still too high for a privacy budget of {target_epsilon}, please use a lower sigma_low."


I would replace "please use a lower sigma_low" with something like:
"you can benefit quality by allowing smaller sigma_low without exceeding target epsilon"

But the current version is also fine.

romovpa · 2022-02-11T17:30:56Z

opacus/accountants/utils.py

    accountant: str = "rdp",
+    epsilon_tolerance: float = 0.01,
+    sigma_low: float = 0.01,


I wanted to ask, why the default sigma_low is so high. We will surprise the user with the warning and suboptimal result if the best sigma is 1e-3 for example.
But then I found that I don't understand what is the point of having this parameter at all? Why not starting with sigma_low=0 always?

This won't hurt this expression target_epsilon - eps_high > epsilon_tolerance. We will never reach this value closer than tolerance/2.

romovpa · 2022-02-11T17:37:38Z

opacus/accountants/utils.py

    accountant: str = "rdp",
+    epsilon_tolerance: float = 0.01,
+    sigma_low: float = 0.01,
+    sigma_high: float = 200,


Why are we so sure that 200 is high enough?

Why not eliminate this constant by probing sigma_high = tol*2^k using this removed algorithm:

sigma_high = tol while eps > target_epsilon: sigma_high = 2 * sigma_high accountant.steps = [(sigma_high, sample_rate, int(epochs / sample_rate))] eps = accountant.get_epsilon(delta=target_delta, **kwargs) if sigma_high > MAX_SIGMA: raise ValueError("The privacy budget is too low.")

Summary: Pull Request resolved: pytorch#348 Noise multiplier now verifies that the actual epsilon is *lower* than the target epsilon. Bounds of the range of search for sigma, and precision can now be given as arguments to get_noise_multiplier. Differential Revision: D34003401 fbshipit-source-id: 93cedb970a44e1cf406834ffa61f34307de43ae1

facebook-github-bot · 2022-02-15T10:23:39Z

This pull request was exported from Phabricator. Differential Revision: D34003401

romovpa

Sweet!
One nit to add a comment.

romovpa · 2022-02-15T11:42:49Z

opacus/accountants/utils.py

-# Noise higher than MAX_SIGMA considered unreasonable
-MAX_SIGMA = 2000
-
+MAX_SIGMA = 1e6


There was a comment before which I recommend to leave because the constant looks a bit surprising.

# Noise level higher than MAX_SIGMA considered unreasonable # leading to "not sufficient privacy budget" exception MAX_SIGMA = 1e6

facebook-github-bot added CLA Signed This label is managed by the Facebook bot. Authors need to sign the CLA before a PR can be reviewed. fb-exported labels Feb 4, 2022

alexandresablayrolles linked an issue Feb 4, 2022 that may be closed by this pull request

The Sigma binary search is not conservative and can overshoot target_epsilon #346

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alexandresablayrolles mentioned this pull request Feb 4, 2022

The Sigma binary search is not conservative and can overshoot target_epsilon #346

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romovpa changed the title ~~Improve get_noise_multiplier~~ Conservative search for target epsilon in get_noise_multiplier Feb 4, 2022

romovpa suggested changes Feb 4, 2022

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alexandresablayrolles force-pushed the export-D34003401 branch from e43d06b to 19d2981 Compare February 10, 2022 13:01

alexandresablayrolles force-pushed the export-D34003401 branch from 19d2981 to affd532 Compare February 11, 2022 14:03

romovpa suggested changes Feb 11, 2022

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alexandresablayrolles force-pushed the export-D34003401 branch from affd532 to ca984ee Compare February 15, 2022 10:23

romovpa approved these changes Feb 15, 2022

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facebook-github-bot closed this in 6dd2495 Feb 16, 2022

ffuuugor mentioned this pull request Apr 27, 2022

Opacus: DP-SGD with massive epsilon does not attain same accuracy as model with DP-SGD #308

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Conservative search for target epsilon in get_noise_multiplier #348

Conservative search for target epsilon in get_noise_multiplier #348

alexandresablayrolles commented Feb 4, 2022 •

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Conservative search for target epsilon in get_noise_multiplier #348

Conservative search for target epsilon in get_noise_multiplier #348

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alexandresablayrolles commented Feb 4, 2022 • edited by romovpa Loading

Problem

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alexandresablayrolles commented Feb 4, 2022 •

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