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One pass learning updates a model with only a single scan of the dataset, without storing historical data. Previous studies focus on classification tasks with a fixed class set, and will perform poorly in an open dynamic environment when new classes emerge in a data stream. The performance degrades because the classifier needs to receive a sufficient number of instances from new classes to establish a good model. This can take a long period of time. In order to reduce this period to deal with any-time prediction task, we introduce a framework to handle emerging new classes called One-Pass Class Incremental Learning (OPCIL). The central issue in OPCIL is: how to effectively adapt a classifier of existing classes to incorporate emerging new classes. We call it the new class adaptation issue, and propose a new approach to address it, which requires only one new class instance. The key is to generate pseudo instances which are optimized to satisfy properties that produce a good discriminative classifier. We provide the necessary propertiesand optimization procedures required to address this issue. Experiments validate the effectiveness of this approach.