# -*- coding: utf-8 -*-
""" The kl-UCB-H policy, for one-parameter exponential distributions.
Reference: [Lai 87](https://projecteuclid.org/download/pdf_1/euclid.aos/1176350495)
"""
from __future__ import division, print_function # Python 2 compatibility
__author__ = "Lilian Besson"
__version__ = "0.1"
from math import log
import numpy as np
np.seterr(divide='ignore') # XXX dangerous in general, controlled here!
try:
from .kullback import klucbBern
from .klUCB import klUCB, c
except ImportError:
from kullback import klucbBern
from klUCB import klUCB, c
[docs]class klUCBH(klUCB):
""" The kl-UCB-H policy, for one-parameter exponential distributions.
Reference: [Lai 87](https://projecteuclid.org/download/pdf_1/euclid.aos/1176350495)
"""
[docs] def __init__(self, nbArms, horizon=None, tolerance=1e-4, klucb=klucbBern, c=c, lower=0., amplitude=1.):
super(klUCBH, self).__init__(nbArms, tolerance=tolerance, klucb=klucb, c=c, lower=lower, amplitude=amplitude)
self.horizon = int(horizon) #: Parameter :math:`T` = known horizon of the experiment.
[docs] def __str__(self):
return r"kl-UCB-H($T={}$, {}{})".format(self.horizon, "" if self.c == 1 else r"$c={:.3g}$".format(self.c), self.klucb.__name__[5:])
[docs] def computeIndex(self, arm):
r""" Compute the current index, at time t and after :math:`N_k(t)` pulls of arm k:
.. math::
\hat{\mu}_k(t) &= \frac{X_k(t)}{N_k(t)}, \\
U_k(t) &= \sup\limits_{q \in [a, b]} \left\{ q : \mathrm{kl}(\hat{\mu}_k(t), q) \leq \frac{c \log(T)}{N_k(t)} \right\},\\
I_k(t) &= U_k(t).
If rewards are in :math:`[a, b]` (default to :math:`[0, 1]`) and :math:`\mathrm{kl}(x, y)` is the Kullback-Leibler divergence between two distributions of means x and y (see :mod:`Arms.kullback`),
and c is the parameter (default to 1).
"""
if self.pulls[arm] < 1:
return float('+inf')
else:
# XXX We could adapt tolerance to the value of self.t
return self.klucb(self.rewards[arm] / self.pulls[arm], self.c * log(self.horizon) / self.pulls[arm], self.tolerance)
[docs] def computeAllIndex(self):
""" Compute the current indexes for all arms, in a vectorized manner."""
indexes = self.klucb_vect(self.rewards / self.pulls, self.c * np.log(self.horizon) / self.pulls, self.tolerance)
indexes[self.pulls < 1] = float('+inf')
self.index[:] = indexes