Constrained discriminative linear transform (CDLT) optimized with Extended Baum-Welch (EBW) has been presented in the literature as a discriminative speaker adaptation method that outperforms the conventional maximum likelihood algorithm. Defining the controlling parameter of EBW to achieve the best performance of speaker adaptation, however, still remains an open question. This paper presents an empirical study on this issue. Results of our experiment suggest that a log-linear relationship exists between the optimal controlling parameter and the amount of data. This relationship can be used to efficiently define the controlling parameter for each test speaker to improve CDLT performance. We also discuss the possibility of generalizing the log-linear rule to a wider range of learning problems because such knowledge can substantially reduce the computation effort for parameter tuning. © 2011 IEEE.