A Stochastic Extension of Hamiltonian Descent Methods


We analyse the recently released work in Maddison et. al. (2018), which employs Hamiltonian dynamics to allow faster convergence rate on a wider class of objectices. The proposed framework allows for linear rates of convergence on certain classes of non-strongly convex functions and generalizes the momentum method to non-classical kinetic energies. We propose a stochastic variant of one such method, and sketch its convergence proof. We also implement the deterministic methods as well as the stochastic counterpart and compare various facets of the methods with baselines such as Gradient Descent and Momentum. Link