Add the option to fix the sampling seed such that the Monte-Carlo expectation always gives the same result.

f should be able to accept keyword arguments

Why was it needed in the first place? Given a differentiable probability distribution constructor $\theta \mapsto p(\theta)$, differentiate through $\theta \mapsto E[c(V)]$ where $V \sim p(\theta)$.

Not directly necessary for Perturbed because we can put $c \circ f$ in the Reinforce, but necessary for regularized because $c \circ f$ is not an LP (not amenable to FW).

struct Pushforward
    fixed_atoms_dist_constructor  # must return a FixedAtomsProbabilityDistribution
    post_processing
end

function (p::Pushforward)(theta)
    dist = p.fixed_atoms_dist_constructor(theta)
    return mean(p.post_processing, dist)
end

Actually it is necessary to define compute_probability_distribution here along with its rrule for Reinforce

https://github.com/JuliaDecisionFocusedLearning/InferOpt.jl/blob/59ab4fe21682e8c0a20bb55d4da3b4cb91f2cc0c/src/perturbed/abstract_perturbed.jl#L118-L153

The Pushforward struct is no longer necessary then

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Differentiating through samples is not defined. Use the square of exp instead

Type or function?

How do we fix one parameter of the distribution?

Implement baseline method