# Policies.klUCB module¶

The generic KL-UCB policy for one-parameter exponential distributions.

Policies.klUCB.c = 1.0

default value, as it was in pymaBandits v1.0

Policies.klUCB.TOLERANCE = 0.0001

Default value for the tolerance for computing numerical approximations of the kl-UCB indexes.

class Policies.klUCB.klUCB(nbArms, tolerance=0.0001, klucb=CPUDispatcher(<function klucbBern>), c=1.0, lower=0.0, amplitude=1.0)[source]

The generic KL-UCB policy for one-parameter exponential distributions.

__init__(nbArms, tolerance=0.0001, klucb=CPUDispatcher(<function klucbBern>), c=1.0, lower=0.0, amplitude=1.0)[source]

New generic index policy.

• nbArms: the number of arms,

• lower, amplitude: lower value and known amplitude of the rewards.

c = None

Parameter c

klucb = None

kl function to use

klucb_vect = None

kl function to use, in a vectorized way using numpy.vectorize().

tolerance = None

Numerical tolerance

__str__()[source]

-> str

computeIndex(arm)[source]

Compute the current index, at time t and after $$N_k(t)$$ pulls of arm k:

$\begin{split}\hat{\mu}_k(t) &= \frac{X_k(t)}{N_k(t)}, \\ U_k(t) &= \sup\limits_{q \in [a, b]} \left\{ q : \mathrm{kl}(\hat{\mu}_k(t), q) \leq \frac{c \log(t)}{N_k(t)} \right\},\\ I_k(t) &= U_k(t).\end{split}$

If rewards are in $$[a, b]$$ (default to $$[0, 1]$$) and $$\mathrm{kl}(x, y)$$ is the Kullback-Leibler divergence between two distributions of means x and y (see Arms.kullback), and c is the parameter (default to 1).

computeAllIndex()[source]

Compute the current indexes for all arms, in a vectorized manner.

__module__ = 'Policies.klUCB'