Title: Adaptive Update Direction Rectification for Unsupervised Continual Learning. Abstract: Recent works on continual learning have shown that unsupervised continual learning (UCL) methods rival or even beat supervised continual learning methods. However, most UCL methods typically adopt fixed learning strategies with pre-defined objectives and ignore the influence of the constant shift of data distributions on the newer training process. This non-adaptive paradigm tends to achieve sub-optimal performance, since the optimal update direction (to ensure the trade-off between old and new tasks) keeps changing during training over sequential tasks. In this work, we thus propose a novel UCL framework termed AUDR to adaptively rectify the update direction by a policy network (i.e., the Actor) at each training step based on the reward predicted by a value network (i.e., the Critic). Concretely, different from existing Actor-Critic based reinforcement learning works, there are three vital designs that make our AUDR applicable to the UCL setting: (1) A reward function to measure the score/value of the currently selected action, which provides the ground-truth reward to guide the Critic's predictions; (2) An action space for the Actor to select actions (i.e., update directions) according to the reward predicted by the Critic; (3) A multinomial sampling strategy with a lower-bound on the sampling probability of each action, which is designed to improve the variance of the Actor's selected actions for more diversified exploration. Extensive experiments show that our AUDR achieves state-of-the-art results under both the in-dataset and cross-dataset UCL settings. Importantly, our AUDR also shows superior performance when combined with other UCL methods, which suggests that our AUDR is highly extensible and versatile.