SPSA: maxiter (int) – The maximum number of iterations. Note that this is not the maximal number of function evaluations

Question

This is from classical optimization algo. used for VQE. May I know what is the difference between maxiter and the number of function evaluation difference?

Answer 1

For every iteration (step) of SPSA, the cost function is evaluated several times (similar principle to other global-optimization algorithms like Particle-Swarm), contributing to the next step.

Also, the details of SPSA can be read from:

• Geeks4Geeks
• The original paper

You can see it yourself by running this code:

#!/usr/bin/env python3
  
import numpy as np
from qiskit.algorithms.optimizers import SPSA
from qiskit.circuit.library import PauliTwoDesign
from qiskit.opflow import Z, StateFn

ansatz = PauliTwoDesign(2, reps=1, seed=2)
observable = Z ^ Z
initial_point = np.random.random(ansatz.num_parameters)

iter = 0

def loss(x):
    bound = ansatz.bind_parameters(x)
    return np.real((StateFn(observable, is_measurement=True) @ StateFn(bound)).eval())

def callbackfun(nevals, params, fval, stepsize, acceptedstep):
    global iter
    print(f'Iteration: {iter} Number of evaluations: {nevals}')
    iter += 1

spsa = SPSA(maxiter=300, callback=callbackfun)
result = spsa.minimize(loss, initial_point)

print(result)