Secretary Problem simulation

secretary_simulation.py

n_trials = 10000
n_candidates = 100
max_burn = int(0.66 * n_candidates) 
for T in range(1, max_burn, 5):
  global_maxes = [] 
  diff_from_max = [] 
  time_taken = []
  final_choices = [] 
  for i in range(n_trials):
    
    candidates = np.random.poisson(lam = 100, size = n_candidates)
    #candidates = weib.random_samples(100).round()
    np.random.shuffle(candidates)
    global_max = np.max(candidates) 
    global_maxes.append(global_max)
    pool = candidates[:T]
    remainder = candidates[T:]
    pool_max = np.max(pool)
    thresh = np.quantile(pool, q = 1.0)
    for i in range(len(remainder)):
      #print(i)
      if remainder[i] > thresh: 
        time_taken.append(T + i)
        diff = global_max - remainder[i]
        diff_from_max.append(diff)
        
        final_choices.append(remainder[i])
        break
  print("Total Candidates:", n_candidates, "|| Burn in Period = ", T, "|| Trials = ", n_trials)
  print("Average Global Max = {:.2f}".format(np.mean(global_maxes)))
  print("Average Choice = {:.2f}".format(np.mean(final_choices)))
  print("Average diff from max {:.2f}".format(np.mean(diff_from_max)), "| Average time taken {:.2f}".format(np.mean(time_taken))), #"| Efficiency {:.2f}".format(np.mean(time_taken/np.mean(diff_from_max))))
  print("------------------------------------------------------------------------------------------------------")