Trajectory Ensembles and Machine Learning: From reinforcement learning for rare event sampling to training of neural network ensembles - Mair, Jamie (2023)
This thesis builds on the existing body of work connecting the fields of statistical mechanics and machine learning. Many advances in machine learning have found their roots in statistical mechanics, e.g. simulated annealing for heuristic optimisation. Primarily, we aim to build bridges between trajectory ensemble techniques and current advances in machine learning, and in particular, deep learning. We explore these connections in two avenues: the first connects the study of rare events with that of reinforcement learning (RL); the second introduces a trajectory sampling algorithm for jointly training an ensemble of neural networks. We derive a framework for translating a rare event sampling problem into the language of RL, offering a way to leverage modern deep RL algorithms to obtain near-optimal sampling dynamics. Our work showcases a plethora of these RL algorithms and provides analysis on examples, including both finite and infinite time problems. Furthermore, we present a novel neural network ensemble training method, facilitated via Markov chain Monte Carlo algorithms, to produce coupled ensembles using gradient-free updates. We show that our coupled ensembles perform better, and are easier to train, than their uncoupled counterparts trained via neuroevolution, providing both analytic results on a linear problem and empirical evidence on the MNIST problem.