Perturbed oracles with variance reduction

[BatyLeo]

This PR reworks all the AbstractPerturbed related structs:

• Most methods (including the rrule) are now generic and implemented directly on AbstractPerturbed
• As a kwarg option enabled by default, gradients can be computed with variance reduction
• Additive and multiplicative perturbations still exist as a special case, and are compatible with Fenchel-Young losses
• Custom distributions can be used for additive and multiplicative perturbations
• New PerturbedOracle layer, generalizing additive/multiplicative perturbations, where the perturbation can have any form. It cannot be used with Fenchel-young losses
• Tests for new options
• New tests checking that a PerturbedOracle with the correct distribution coincides with PerturbedAdditive and PerturbedMultiplicative

[codecov-commenter]

Codecov Report

Patch coverage: 91.22% and project coverage change: +0.67% :tada:

Comparison is base (44a3055) 84.75% compared to head (1e0d8ec) 85.42%. Report is 3 commits behind head on main.

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Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #80 +/- ## ========================================== + Coverage 84.75% 85.42% +0.67% ========================================== Files 18 19 +1 Lines 341 391 +50 ========================================== + Hits 289 334 +45 - Misses 52 57 +5 ``` | [Files Changed](https://app.codecov.io/gh/axelparmentier/InferOpt.jl/pull/80?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=None) | Coverage Δ | | |---|---|---| | [src/InferOpt.jl](https://app.codecov.io/gh/axelparmentier/InferOpt.jl/pull/80?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=None#diff-c3JjL0luZmVyT3B0Lmps) | `100.00% <ø> (ø)` | | | [src/perturbed/perturbed\_oracle.jl](https://app.codecov.io/gh/axelparmentier/InferOpt.jl/pull/80?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=None#diff-c3JjL3BlcnR1cmJlZC9wZXJ0dXJiZWRfb3JhY2xlLmps) | `85.71% <85.71%> (ø)` | | | [src/perturbed/abstract\_perturbed.jl](https://app.codecov.io/gh/axelparmentier/InferOpt.jl/pull/80?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=None#diff-c3JjL3BlcnR1cmJlZC9hYnN0cmFjdF9wZXJ0dXJiZWQuamw=) | `86.20% <88.00%> (-3.80%)` | :arrow_down: | | [src/perturbed/additive.jl](https://app.codecov.io/gh/axelparmentier/InferOpt.jl/pull/80?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=None#diff-c3JjL3BlcnR1cmJlZC9hZGRpdGl2ZS5qbA==) | `88.23% <93.33%> (+4.90%)` | :arrow_up: | | [src/perturbed/multiplicative.jl](https://app.codecov.io/gh/axelparmentier/InferOpt.jl/pull/80?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=None#diff-c3JjL3BlcnR1cmJlZC9tdWx0aXBsaWNhdGl2ZS5qbA==) | `88.23% <93.33%> (+4.90%)` | :arrow_up: | | [src/imitation/fenchel\_young\_loss.jl](https://app.codecov.io/gh/axelparmentier/InferOpt.jl/pull/80?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=None#diff-c3JjL2ltaXRhdGlvbi9mZW5jaGVsX3lvdW5nX2xvc3Muamw=) | `87.75% <100.00%> (ø)` | |

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[gdalle]

I won't have time to review this, and I probably need to take a step back to focus on my own research. It would be nice if you and @LouisBouvier could rely on each other for PR reviewing, can you bring him up to speed?

[gdalle]

As far as custom distributions are concerned, it would be nice but we need a gradlogpdf function if memory serves me well. This is not necessarily easy to find

[gdalle]

And I agree that Fenchel Young is messy. This implementation tried to minimize code duplication, but possibly at the expense of clarity.

[BatyLeo]

As far as custom distributions are concerned, it would be nice but we need a gradlogpdf function if memory serves me well. This is not necessarily easy to find

The gradlogpdf can either be given by the user or computed with autodiff, this is already the case in the new generic PerturbedOracle struct, but it cannot be used with FenchelYoungLoss at the moment

[gdalle]

The gradlogpdf can either be given by the user or computed with autodiff

Will we have a problem with nested autodiff?

[gdalle]

Maybe to avoid random failures across Julia versions we could use StableRNGs in testing?

[BatyLeo]

The gradlogpdf can either be given by the user or computed with autodiff

Will we have a problem with nested autodiff?

What do you mean by "nested autodiff" ?

Maybe to avoid random failures across Julia versions we could use StableRNGs in testing?

I'm still investigating, but it seems that even whithin the same Julia versions our tests are not deterministic. The failing test passes on my laptop about half the time

[gdalle]

What do you mean by "nested autodiff" ?

Differentiating something with Zygote that has already been differentiated with it once. I don't think it will be the case here

[BatyLeo]

Should we enable variance reduction by default ? Currently it is not.

[gdalle]

We're gonna tag a breaking release anyway, we might as well

[LouisBouvier]

Can we use variance reduction also in FY loss ? We also estimate an expectation by Monte-Carlo, when we use more than one sample we could think about it ?

[gdalle]

Since questions are popping up on the Julia forum, is this ready to go?

[BatyLeo]

Since questions are popping up on the Julia forum, is this ready to go?

I think it is, Louis already reviewed it. Maybe check the AbstractPerturbed rrule once more ?

[gdalle]

I trust you guys, you do the merge this time ;)

[gdalle]

Congrats, this was huge work!