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Importance Sampling
We have two sources D_{1}(x) and D_{2}(x) that produce differnt distributions.
We compute expectation of a function F(x) on one source while sampling the other source. The
expectation of F(x) with respect to distribution D is the sum of products of all values of X
with the probability that D assigns that value. In our case:
E_{D2}[F(x)] =
=
=
E_{D1}[(
)F(x)]
EXAMPLE 1
Input:

F(x) = k.


Computation:
 We find expectancy
E_{D2}[k] from samples of D_{1}.
 We check the equation by computing
E_{D2}[F(x)].
=
=
=
E_{D1}[k]
 One of the problems in importance sampling is the variance.
In this case.
=
=
=
Yishay Mansour
20000107