Classification has been commonly used in many data mining projects in the financial service industry. For instance, to predict collectability of accounts receivable, a binary class label is created based on whether a payment is received within a certain period. However, optimization of the classifier does not necessarily lead to maximization of return on investment (ROI), since maximization of the true positive rate is often different from maximization of the collectable amount which determines the ROI under a fixed budget constraint. The typical cost sensitive learning does not solve this problem either since it involves an unknown opportunity cost due to the budget constraint. Learning the ranks of collectable amount would ultimately solve the problem, but it tries to tackle an unnecessarily difficult problem and often results in poorer results for our specific target. We propose a new algorithm that uses gradient descent to directly optimize the related monetary measure under the b...