python - How to use nevergrad to find the minimum of a cost function over the field of integers?

Question

As part of our Poolkeh paper, we thought to use nevergrad. However, sadly it doesn't always return the same result, nor the most optimal one.

We tried DiscreteOnePlusOne as an optimizer, but it didn't find the optimal results. OnePlusOne worked ok, but didn't give the best solution and it needed some hints like this one:

if s1 < s2*(1+r0):
    return np.Inf

We explored the case of pooling COVID-19 tests with two steps, here is the complete code:

!pip install nevergrad
import numpy as np
def optimal(r0: float, s1:int, s2:int):
  r0 = r0/100
  if s1 < s2*(1+r0):
    return np.Inf

  p1=1-np.power(1-r0,s1)
  r1=r0/p1
  p2=1-np.power(1-r1,s2)
  return 1/s1 + p1/s2 + p1*p2

import nevergrad as ng

def findBestStategy(r0: float):
  '''
  r0 is in %
  '''
  parametrization = ng.p.Instrumentation(
      r0 = r0, 
      s1=ng.p.Scalar(lower=1, upper=100).set_integer_casting(),
      s2=ng.p.Scalar(lower=1, upper=100).set_integer_casting(),
  )
  optimizer = ng.optimizers.OnePlusOne(parametrization=parametrization, budget=2000, num_workers=1)
  recommendation = optimizer.minimize(optimal)
  return recommendation.kwargs
findBestStategy(1)
{'r0': 1, 's1': 23, 's2': 5}

This is not the optimal, but really it's close :

optimal(1, 23,5)
0.13013924406458133
optimal(1, 24,5) 
0.13007783167425113

1. How can we make nevergrad more robust?
2. Which optimizer should we use?
3. Is there a way to run nevergrad multiple times with different "initial conditions" and take the optimal results among all multiple tries?

标签： pythonpython-3.xmathematical-optimizationnevergrad