平均志向が最悪の環境 https://scrapbox.io/nishio/%E5%B9%B3%E5%9D%87%E5%BF%97%E5%90%91%E3%81%8C%E6%9C%80%E6%82%AA%E3%81%AE%E7%92%B0%E5%A2%83

t.py

# -*- encoding: utf-8 -*-
import numpy as np
from collections import Counter
N = 100
D = 2
p = 0.5
q = 0.3
NUM_ITER = 100000

def score(actions, axis):
    score = actions.dot(axis)
    ret = np.zeros(N)
    best = score.argsort()[:int(N * q)]
    ret[best] = 1
    return ret

def test():
    buf = np.zeros((NUM_ITER, 3))
    for i in range(NUM_ITER):
        actions = np.random.normal(size=(N, D))
        observable = np.random.binomial(1, p, size=N)
        observed_actions = actions[observable == 1]
        mean = observed_actions.mean(0)
        axis = np.random.normal(size=D)
        original = actions[0].copy()

        for j, eta in enumerate([0.0, 0.5, -1.0]):
            actions[0] = original + (mean - original) * eta
            buf[i, j] = score(actions, axis)[0]

    print(buf.mean(0))


test()