API walkthrough
The function derivative_estimate transforms a stochastic program containing discrete randomness into a new program whose average is the derivative of the original.
StochasticAD.derivative_estimate — Functionderivative_estimate(X, p::Real; backend=StochasticAD.PrunedFIs)Computes an unbiased estimate of $\frac{\mathrm{d}\mathbb{E}[X(p)]}{\mathrm{d}p}$, the derivative of the expectation of the random function X(p) with respect to its input p. The backend keyword argument describes the algorithm used by the third component of the stochastic triple, see Technical details for more details.
While derivative_estimate is self-contained, we can also use the functions below to work with stochastic triples directly.
StochasticAD.stochastic_triple — Functionstochastic_triple(X, p::Real; kwargs...)
stochastic_triple(p::Real; kwargs...)Return the result of propagating the stochastic triple p + ε through the random function X(p). When X is not provided, the identity function is used, i.e. the triple p + ε is returned.
StochasticAD.derivative_contribution — Functionderivative_contribution(st::StochasticTriple)Return the derivative estimate given by combining the dual and triple components of st.
StochasticAD.value — Functionvalue(st::StochasticTriple)Return the primal value of st.
StochasticAD.delta — Functiondelta(st::StochasticTriple)Return the almost-sure derivative of st, i.e. the rate of infinitesimal change.
StochasticAD.perturbations — Functionperturbations(st::StochasticTriple)Return the finite perturbation(s) of st, in a format dependent on the backend used for storing perturbations.
Note that derivative_estimate is simply the composition of stochastic_triple and derivative_contribution.
Smoothing
What happens if we run derivative_contribution after each step, instead of only at the end? This is smoothing, which combines the second and third components of a single stochastic triple into a single dual component. Smoothing no longer has a guarantee of unbiasedness, but is surprisingly accurate in a number of situations.
[Smoothing functionality coming soon.]
Optimization
We also provide utilities to make it easier to get started with forming and training a model via stochastic gradient descent:
StochasticAD.StochasticModel — TypeStochasticModel(p, X)Combine stochastic program X with parameter p into a trainable model using Functors (formulate as a minimization problem, i.e. find $p$ that minimizes $\mathbb{E}[X(p)]$).
StochasticAD.stochastic_gradient — Functionstochastic_gradient(m::StochasticModel)Compute gradient with respect to the trainable parameter p of StochasticModel(p, X)
These are used in the tutorial on stochastic optimization.