  The paper deals with the non-parametric estimation in the regression with the
multiplicative noise. Using the local polynomial fitting and the bayesian
approach, we construct the minimax on isotropic H\"older class estimator. Next
applying Lepski's method, we propose the estimator which is optimally adaptive
over the collection of isotropic H\"older classes. To prove the optimality of
the proposed procedure we establish, in particular, the exponential inequality
for the deviation of locally bayesian estimator from the parameter to be
estimated. These theoretical results are illustrated by simulation study.
