# -*- coding: utf-8 -*-
r""" The UCB+ policy for bounded bandits, with a small trick on the index.
- Reference: [Auer et al. 2002], and [[Garivier et al. 2016](https://arxiv.org/pdf/1605.08988.pdf)] (it is noted :math:`\mathrm{UCB}^*` in the second article).
"""
from __future__ import division, print_function # Python 2 compatibility
__author__ = "Lilian Besson"
__version__ = "0.9"
from math import sqrt, log
import numpy as np
np.seterr(divide='ignore') # XXX dangerous in general, controlled here!
try:
from .UCB import UCB
except ImportError:
from UCB import UCB
[docs]class UCBplus(UCB):
r""" The UCB+ policy for bounded bandits, with a small trick on the index.
- Reference: [Auer et al. 2002], and [[Garivier et al. 2016](https://arxiv.org/pdf/1605.08988.pdf)] (it is noted :math:`\mathrm{UCB}^*` in the second article).
"""
[docs] def __str__(self):
return "UCB+"
[docs] def computeIndex(self, arm):
r""" Compute the current index, at time t and after :math:`N_k(t)` pulls of arm k:
.. math:: I_k(t) = \frac{X_k(t)}{N_k(t)} + \sqrt{\max\left(0, \frac{\log(t / N_k(t))}{2 N_k(t)}\right)}.
"""
if self.pulls[arm] < 1:
return float('+inf')
else:
return (self.rewards[arm] / self.pulls[arm]) + sqrt(max(0., log(self.t / (self.pulls[arm]))) / (2 * self.pulls[arm]))
[docs] def computeAllIndex(self):
""" Compute the current indexes for all arms, in a vectorized manner."""
indexes = (self.rewards / self.pulls) + np.sqrt(np.maximum(0., (2 * np.log10(self.t)) / self.pulls))
indexes[self.pulls < 1] = float('+inf')
self.index[:] = indexes