Before revision:  We consider a semi-parametric model where the relationship between the expectation of the log of valuation and the covariates is linear (hence parametric) and the residual uncertainty distribution , i. e., the noise distribution , is non-parametric . We develop a pricing policy, DEEP-C, which learns this relationship with minimal exploration and in turn achieves optimal regretasymptotically in the time horizon\tilde  .
After revision:  We consider a semi-parametric model where the relationship between the expectation of the log of valuation and the covariates is linear (hence parametric) and the residual uncertainty distribution , i. e., the noise distribution , is non-parametric and provide the first algorithm which learns both regression parameters and residual distribution with\tilde .