Data mining and Machine Learning research has led to a wide variety of training methods and algorithms for different types of models. Many of these methods solve or approximate NP-hard optimization problems at their core, using vastly different approaches, some algebraic, others heuristic. This paper demonstrates another way of solving these problems by reducing them to quadratic polynomial optimization problems on binary variables. This class of parametric optimization problems is well-researched and powerful, and offers a unifying framework for many relevant ML problems that can all be tackled with one efficient solver. Because of the friendly domain of binary values, such a solver lends itself particularly well to hardware acceleration, as we further demonstrate in this paper by evaluating our problem reductions using FPGAs.