Relativistic Monte Carlo @ BDL2016

Our work (joint work with Xiaoyu Lu, Valerio Perrone, Sebastian Vollmer and Yee Whye Teh) on relativistic Monte Carlo was accepted as a contributed talk at the Bayesian Deep Learning Workshop at NIPS 2016. Come along at 11:20am on December 10 when Valerio and Xiaoyu will be presenting our work.

We are excited about Relativistic Monte Carlo as a way to derive an MCMC algorithm more robust to hyperparameter choice. Here is the abstract:

Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time discretizations and performs poorly if there is a mismatch between the spatial geometry of the target distribution and the scales of the momentum distribution. In particular the mass matrix of HMC is hard to tune well. In order to alleviate these problems we propose relativistic Hamiltonian Monte Carlo, a version of HMC based on relativistic dynamics that introduce a maximum velocity on particles. We also derive stochastic gradient versions of the algorithm and show that the resulting algorithms bear interesting relationships to gradient clipping, RMSprop, Adagrad and Adam, popular optimisation methods in deep learning. Based on this, we develop relativistic stochastic gradient descent by taking the zero-temperature limit of relativistic stochastic gradient Hamiltonian Monte Carlo. In experiments we show that the relativistic algorithms perform better than classical Newtonian variants and Adam.