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http://nhiro.org.s3.amazonaws.com/8/0/80477c9087b5a7b4a0515324bf429917.jpg https://gyazo.com/80477c9087b5a7b4a0515324bf429917

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113

Gaussian Process UCB

GPはsklearnに実装が

ある

fitしてpredictすると平均と分散が返ってくるので

あらかじめ計算しておいた定数βを掛けてargmax

Theorem 1 Let

2log(D|t2n2/66).

a sample f of a GP with mean function zero and

covariance function k(x, x'), we obtain a regret bound Algorit hm 1 The GP-UCB algorithm.

of O(TYT log|D|) with high probability. Precisely,

(0, 1) and Bt

Running GP-UCB with B for

=

Input: Input space D; GP Prior Ho

for t 1,2,. do

Choose targmax t-1(x)+ Vrot-1(x)

= 0, oo

k

Pr{Rr s VCTBr VT21}21-&.

ED

Sample yf(X,) + €

Perform Bayesian update to obtain

end for

and ot

where Ci 8/log(1 + o2).

learn.org/stable/modules/generated/sklearn.gaussian process.GaussianProcess.html