Simulate effective sample size computation to check the example given in "Lessors from Contextual Bandit Learning in a Customer Support Bot" by Karampatziakis et al.

effective_sample_size.py

import numpy as np
k = 20
eps = 0.1
eps2 = 0.5
w = []
n = 100000
for i in range(n):
    rule = np.random.choice(k)
    
    eps_greedy_action = rule if np.random.rand() > eps else np.random.choice(k)
    mu = (1 - eps + eps/k) if rule == eps_greedy_action else eps/k
    
    pi_action = eps_greedy_action if np.random.rand() > eps2 else np.random.choice(k)
    pi = (1 - eps2 + eps2/k) if pi_action == eps_greedy_action else eps2/k
    
    w.append(pi/mu)

w = np.array(w)
print((w.sum() ** 2) / (w * w).sum() / n)
# 0.0594