Multi-task learning (MTL) aims to improve the performance of a primary task by jointly learning with related auxiliary tasks. Traditional MTL methods select tasks randomly during training. However, both previous studies and our results suggest that such the random selection of tasks may not be helpful, and can even be harmful to performance. Therefore, new strategies for task selection and assignment in MTL need to be explored. This paper studies the multi-modal, multi-task dialogue act classification task, and proposes a method for selecting and assigning tasks based on non-stationary multi-armed bandits (MAB) with discounted Thompson Sampling (TS) using Gaussian priors. Our experimental results show that in different training stages, different tasks have different utility. Our proposed method can effectively identify the task utility, actively avoid useless or harmful tasks, and realise the task assignment during training. Our proposed method is significantly superior in terms of UAR and F1 to the single-task and multi-task baselines with p-values < 0.05. Further analysis of experiments indicates that for the dataset with the data imbalance problem, our proposed method has significantly higher stability and can obtain consistent and decent performance for minority classes. Our proposed method is superior to the current state-of-the-art model.