Policies.klUCBHPlus module¶
The improved kl-UCB-H+ policy, for one-parameter exponential distributions. Reference: [Lai 87](https://projecteuclid.org/download/pdf_1/euclid.aos/1176350495)
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class
Policies.klUCBHPlus.klUCBHPlus(nbArms, horizon=None, tolerance=0.0001, klucb=CPUDispatcher(<function klucbBern>), c=1.0, lower=0.0, amplitude=1.0)[source]¶ Bases:
Policies.klUCB.klUCBThe improved kl-UCB-H+ policy, for one-parameter exponential distributions. Reference: [Lai 87](https://projecteuclid.org/download/pdf_1/euclid.aos/1176350495)
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__init__(nbArms, horizon=None, 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.
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horizon= None¶ Parameter \(T\) = known horizon of the experiment.
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computeIndex(arm)[source]¶ Compute the current index, at time t and after \(N_k(t)\) pulls of arm k:
\[\begin{split}\hat{\mu}_k(t) &= \frac{X_k(t)}{N_k(t)}, \\ U_k(t) &= \sup\limits_{q \in [a, b]} \left\{ q : \mathrm{kl}(\hat{\mu}_k(t), q) \leq \frac{c \log(T / N_k(t))}{N_k(t)} \right\},\\ I_k(t) &= U_k(t).\end{split}\]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).
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__module__= 'Policies.klUCBHPlus'¶
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