Title: Continual Invariant Risk Minimization. Abstract: Empirical risk minimization can lead to poor generalization behaviour on unseen environments if the learned model does not capture invariant feature represen- tations. Invariant risk minimization (IRM) is a recent proposal for discovering environment-invariant representations. It was introduced by Arjovsky et al. (2019) and extended by Ahuja et al. (2020). The assumption of IRM is that all environ- ments are available to the learning system at the same time. With this work, we generalize the concept of IRM to scenarios where environments are observed se- quentially. We show that existing approaches, including those designed for contin- ual learning, fail to identify the invariant features and models across sequentially presented environments. We extend IRM under a variational Bayesian and bilevel framework, creating a general approach to continual invariant risk minimization. We also describe a strategy to solve the optimization problems using a variant of the alternating direction method of multiplier (ADMM). We show empirically us- ing multiple datasets and with multiple sequential environments that the proposed methods outperforms or is competitive with prior approaches.