We propose a method to train a cascade of classifiers by simultaneously optimizing all its stages. The approach relies on the idea of optimizing soft cascades. In particular, instead of optimizing a deterministic hard cascade, we optimize a stochastic soft cascade where each stage accepts or rejects samples according to a probability distribution induced by the previous stage-specific classifier. The overall system accuracy is maximized while explicitly controlling the expected cost for feature acquisition. Experimental results on three clinically relevant problems show the effectiveness of our proposed approach in achieving the desired tradeoff between accuracy and feature acquisition cost.