In the corresponding paper, we use the recently develop DeepInference architecture as a general likelihood-free method to estimate parameters of cognitive models. DeepInference is a machine-learning algorithm based on the training of convolutional neural networks. In a first step, the network has to be trained with simulated data to learn the relation of parameters and data. Then, the trained network can be used to re-estimate parameters for real data. The efficiency and robustness of this approach was tested for two decision models based on continuous evidence accumulation. Study 1 investigated the recovery of parameters of the diffusion model, and Study 2 addressed the same question for a Lévy-Flight model. Results demonstrate that the machine-learning approach is superior to traditional multidimensional search algorithms that maximize the likelihood, both in terms of correlations of estimated parameters with true parameters and with regard to absolute deviations. The new approach also excels the maximum likelihood based search pertaining the robustness in the presence of contaminated data.