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Beta-distribution Bandit
from numpy import *
from scipy.stats import beta
class BetaBandit(object):
def __init__(self, num_options=2, prior=(1.0,1.0)):
self.trials = zeros(shape=(num_options,), dtype=int)
self.successes = zeros(shape=(num_options,), dtype=int)
self.num_options = num_options
self.prior = prior
def add_result(self, trial_id, success):
self.trials[trial_id] = self.trials[trial_id] + 1
if (success):
self.successes[trial_id] = self.successes[trial_id] + 1
def get_recommendation(self):
sampled_theta = []
for i in range(self.num_options):
#Construct beta distribution for posterior
dist = beta(self.prior[0]+self.successes[i],
self.prior[1]+self.trials[i]-self.successes[i])
#Draw sample from beta distribution
sampled_theta += [ dist.rvs() ]
# Return the index of the sample with the largest value
return sampled_theta.index( max(sampled_theta) )
from beta_bandit import *
from numpy import *
from scipy.stats import beta
import random
theta = (0.25, 0.35)
def is_conversion(title):
if random.random() < theta[title]:
return True
else:
return False
conversions = [0,0]
trials = [0,0]
N = 100000
trials = zeros(shape=(N,2))
successes = zeros(shape=(N,2))
bb = BetaBandit()
for i in range(N):
choice = bb.get_recommendation()
trials[choice] = trials[choice]+1
conv = is_conversion(choice)
bb.add_result(choice, conv)
trials[i] = bb.trials
successes[i] = bb.successes
from pylab import *
subplot(211)
n = arange(N)+1
loglog(n, trials[:,0], label="title 0")
loglog(n, trials[:,1], label="title 1")
legend()
xlabel("Number of trials")
ylabel("Number of trials/title")
subplot(212)
semilogx(n, (successes[:,0]+successes[:,1])/n, label="CTR")
semilogx(n, zeros(shape=(N,))+0.35, label="Best CTR")
semilogx(n, zeros(shape=(N,))+0.30, label="Random chance CTR")
semilogx(n, zeros(shape=(N,))+0.25, label="Worst CTR")
axis([0,N,0.15,0.45])
xlabel("Number of trials")
ylabel("CTR")
legend()
show()
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