Systems and methods are disclosed for distributed first- or higher-order model fitting algorithms. Determination of the parameter set for the objective function is divided into a plurality of sub-processes, each performed by one of a plurality of worker computers. A master computer coordinates the operation of the plurality of worker computers, each operating on a portion of the parameter set such that no two worker computers contain exactly the same parameter subset nor the complete parameter set. Each worker computer performs its sub-processes on its parameter subset, together with training data. For maximum efficiency, the sub-processes are performed using a compact set of instruction primitives. The results are evaluated by the master computer, which may coordinate additional sub-process operations to perform higher-order optimization or terminate the optimization method and proceed to formulation of a model function.