Although optimization is the longstanding algorithmic backbone of machine learning, new models still require the time-consuming implementation of new solvers. As a result, there are thousands of implementations of optimization algorithms for machine learning problems. A natural question is, if it is always necessary to implement a new solver, or if there is one algorithm that is sufficient for most models. Common belief suggests that such a one-algorithm-fits-all approach cannot work, because this algorithm cannot exploit model specific structure and thus cannot be efficient and robust on a wide variety of problems. Here, we challenge this common belief. We have designed and implemented the optimization framework GENO (GENeric Optimization) that combines a modeling language with a generic solver. GENO generates a solver from the declarative specification of an optimization problem class. The framework is flexible enough to encompass most of the classical machine learning problems. We show on a wide variety of classical but also some recently suggested problems that the automatically generated solvers are (1) as efficient as well-engineered specialized solvers, (2) more efficient by a decent margin than recent state-of-the-art solvers, and (3) orders of magnitude more efficient than classical modeling language plus solver approaches.

Neural Information Processing Systems http://nips.cc/

Although optimization is the longstanding algorithmic backbone of machine learning, new models still require the time-consuming implementation of new solvers. As a result, there are thousands of implementations of optimization algorithms for machine learning problems. A natural question is, if it is always necessary to implement a new solver, or if there is one algorithm that is sufficient for most models. Common belief suggests that such a one-algorithm-fits-all approach cannot work, because this algorithm cannot exploit model specific structure and thus cannot be efficient and robust on a wide variety of problems. Here, we challenge this common belief. We have designed and implemented the optimization framework GENO (GENeric Optimization) that combines a modeling language with a generic solver. GENO generates a solver from the declarative specification of an optimization problem class. The framework is flexible enough to encompass most of the classical machine learning problems. We show on a wide variety of classical but also some recently suggested problems that the automatically generated solvers are (1) as efficient as well-engineered specialized solvers, (2) more efficient by a decent margin than recent state-of-the-art solvers, and (3) orders of magnitude more efficient than classical modeling language plus solver approaches.

Optimization is an integral part of most machine learning systems and most numerical optimization schemes rely on the computation of derivatives. Therefore, frameworks for computing derivatives are an active area of machine learning research. Surprisingly, as of yet, no existing framework is capable of computing higher order matrix and tensor derivatives directly. Here, we close this fundamental gap and present an algorithmic framework for computing matrix and tensor derivatives that extends seamlessly to higher order derivatives. The framework can be used for symbolic as well as for forward and reverse mode automatic differentiation. Experiments show a speedup of up to two orders of magnitude over state-of-the-art frameworks when evaluating higher order derivatives on CPUs and a speedup of about three orders of magnitude on GPUs.