Lifelong Variational Autoencoder via Online Adversarial Expansion Strategy

The Variational Autoencoder (VAE) suffers from a significant loss of information when trained on a non-stationary data distribution. This loss in VAE models, called catastrophic forgetting, has not been studied theoretically before. We analyse the forgetting behaviour of a VAE in continual generative modelling by developing a new lower bound on the data likelihood, which interprets the forgetting process as an increase in the probability distance between the generator's distribution and the evolved data distribution. The proposed bound shows that a VAE-based dynamic expansion model can achieve better performance if its capacity increases appropriately considering the shift in the data distribution. Based on this analysis, we propose a novel expansion criterion that aims to preserve the information diversity among the VAE components, while ensuring that it acquires more knowledge with fewer parameters. Specifically, we implement this expansion criterion from the perspective of a multi-player game and propose the Online Adversarial Expansion Strategy (OAES), which considers all previously learned components as well as the currently updated component as multiple players in a game, while an adversary model evaluates their performance. The proposed OAES can dynamically estimate the discrepancy between each player and the adversary without accessing task information. This leads to the gradual addition of new components while ensuring the knowledge diversity among all of them. We show theoretically and empirically that the proposed extension strategy can enable a VAE model to achieve the best performance given an appropriate model size.