Proposal: change noise syntax

[odow]

@rhsnoise(sp, w=[1,2,3], 2x+y<=w)
# becomes
@rhsnoise(sp, [1,2,3], w->2x+y<=w)

This sorts out the using different noise fiasco since we can just throw new observations into the function (ref #10). It plays nicer with namespacing issues

w = 0
@rhsnoise(sp, w=[1,2,3], 2x+y<=w)
# what is w? 3!

w = 0
@rhsnoise(sp, [1,2,3], w->2x+y<=w)
# what is w? 0!

And is probably a good start towards noises in the constraint coefficients. It also slightly unifies our price interpolation stuff since we would have

@stageobjective(sp, [1,2,3], w->w*x)
# and
@stageobjective(sp, p->p*x)

But we should really have

@stageobjective(sp, [1,2,3], (p, w) -> p*x + w)

to allow for stagewise independent noise on-top-of the price states.

Nothing actionable yet, leaving this as a reminder.

[odow]

Ref. jump-dev/JuMP.jl#1241

[odow]

I thought of this today. It is a whole lot simpler and allows us to more easily modify subproblems.

SDDPModel() do sp, t
    @state(sp, x, x0==0)
    c = @constraint(m, x == 1)
    @stageobjective(m, x)
    parameterize!(sp, [0.5, 0.2, 0.3]) do noise
        rhs = [1.1, 1.2, 1.3]
        JuMP.setRHS(c, rhs[noise])
        @stageobjective(m, noise * x)  # not sure about this
    end
end

This would get rid of @rhsnoise and the @stageobjective that has a noise. Other pro, this plays nice with out-of-sample noise terms (ref #80).

Con: can you have to calls to parameterize!?

To follow up, can we just use @objective and check before a solve if we have added the cost-to-go variable?