  A method to estimate an acoustic field from discrete microphone measurements
is proposed. A kernel-interpolation-based method using the kernel function
formulated for sound field interpolation has been used in various applications.
The kernel function with directional weighting makes it possible to incorporate
prior information on source directions to improve estimation accuracy. However,
in prior studies, parameters for directional weighting have been empirically
determined. We propose a method to optimize these parameters using observation
values, which is particularly useful when prior information on source
directions is uncertain. The proposed algorithm is based on discretization of
the parameters and representation of the kernel function as a weighted sum of
sub-kernels. Two types of regularization for the weights, $L_1$ and $L_2$, are
investigated. Experimental results indicate that the proposed method achieves
higher estimation accuracy than the method without kernel learning.
