Cost vs iterations plot

[raulconchello]

Description

Now when you call q.results.plot_cost() you get a plot of cost vs number of function evaluations. Like the following:

It could be interesting to have another method that plots cost vs number of iterations, so as to see the cost at the end of each iteration of the classical optimizer.

[Q-lds]

How would we do this? We would need:

• a counter-label that indicates which indexes within the cost array belong to the give optimisation round
• a way to average(?) over these multiple costs to provide a plot

The first part is easy (I think), but the second one ... I mean, that is optimiser dependent and it may not be trivial.

[raulconchello]

With @vishal-ph, we thought it could be nice to have this method when we were looking at a graph like the following:

Here the maxiter was 20, so only 20 iterations have been performed but 250 evaluations are displayed. It is rather difficult to see the actual evolution.

I don't think we need to do the average, but just take the last evaluation of each step. This one is the optimized cost if we stop the optimization at that iteration.

For example for spsa:

def SPSA(...):
    ...
    def grad_SPSA(params, c):
        delta = (2*np.random.randint(0, 2, size=len(params))-1)
        return np.real((fun(params + c*delta) - fun(params - c*delta))*delta/(2*c))
    ...
    while improved and not stop and niter < maxiter:
        improved = False
        niter += 1

        # gain sequences
        a = a/(A+niter+1)**alpha
        c = c/(niter+1)**gamma

        # compute gradient descent step
        testx = testx - a*grad_SPSA(testx, c)
        testy = np.real(fun(testx, *args))

        if np.abs(besty-testy) < tol:
            improved = False

        else:
            besty = testy
            bestx = testx
            improved = True

        ...

    return OptimizeResult(fun=besty, x=bestx ....))

You would plot the variable besty vs niter