Developing a robust and sustainable system is an important problem in which deep learning models are used in real-world applications. Ensemble methods combine diverse models to improve performance and achieve robustness. The analysis of time series data requires dealing with continuously incoming instances; however, most ensemble models suffer when adapting to a change in data distribution. Therefore, we propose an on-line ensemble deep learning algorithm that aggregates deep learning models and adjusts the ensemble weight based on loss value in this study. We theoretically demonstrate that the ensemble weight converges to the limiting distribution, and, thus, minimizes the average total loss from a new regret measure based on adversarial assumption. We also present an overall framework that can be applied to analyze time series. In the experiments, we focused on the on-line phase, in which the ensemble models predict the binary class for the simulated data and the financial and non-financial real data. The proposed method outperformed other ensemble approaches. Moreover, our method was not only robust to the intentional attacks but also sustainable in data distribution changes. In the future, our algorithm can be extended to regression and multiclass classification problems.
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