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Machine learning models based on Deep Neural Networks (DNNs) are increasingly deployed in a wide range of applications ranging from self-driving cars to COVID-19 treatment discovery. To support the computational power necessary to learn a DNN, cloud environments with dedicated hardware support have emerged as critical infrastructure. However, there are many integrity challenges associated with outsourcing computation. Various approaches have been developed to address these challenges, building on trusted execution environments (TEE). Yet, no existing approach scales up to support realistic integrity-preserving DNN model training for heavy workloads (deep architectures and millions of training examples) without sustaining a significant performance hit. To mitigate the time gap between pure TEE (full integrity) and pure GPU (no integrity), we combine random verification of selected computation steps with systematic adjustments of DNN hyper-parameters (e.g., a narrow gradient clipping range), hence limiting the attacker's ability to shift the model parameters significantly provided that the step is not selected for verification during its training phase. Experimental results show the new approach achieves 2X to 20X performance improvement over pure TEE based solution while guaranteeing a very high probability of integrity (e.g., 0.999) with respect to state-of-the-art DNN backdoor attacks.