This work introduces TrimTuner – the first system for optimizing machine learning jobs in the cloud by exploiting sub-sampling techniques to reduce the cost of the optimization process, while keeping into account user-specified constraints. TrimTuner jointly optimizes the cloud and application-specific parameters and, unlike state of the art works for cloud optimization, eschews the need to train the model with the full training set every time a new configuration is sampled. Indeed, by leveraging sub-sampling techniques and datasets that are up to 60x smaller than the original one, we show that TrimTuner can reduce the cost of the optimization process by up to 50x. Further, TrimTuner speeds-up the recommendation process by 65x with respect to state of the art techniques for hyperparameter optimization that use sub-sampling techniques. The reasons for this improvement are twofold: i) a novel domain specific heuristic that reduces the number of configurations for which the acquisition function has to be evaluated; ii) the adoption of an ensemble of decision trees that enables boosting the speed of the recommendation process by one additional order of magnitude.