High Dimensional Optimization through the Lens of Machine Learning
It addresses the theoretical understanding of optimization methods for machine learning practitioners, but is incremental as it reviews and explains existing methods.
This thesis reviews numerical optimization methods for high-dimensional machine learning problems, focusing on stochastic gradient descent and momentum methods, and provides convergence proofs for convex functions to explain their success.
This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic models to figure out which methods are suited for non-convex optimization, and develop convergence proofs on convex functions for this selection of methods. With this theoretical foundation for stochastic gradient descent and momentum methods, we try to explain why the methods used commonly in the machine learning field are so successful. Besides explaining successful heuristics, the last chapter also provides a less extensive review of more theoretical methods, which are not quite as popular in practice. So in some sense this work attempts to answer the question: Why are the default Tensorflow optimizers included in the defaults?