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Face authentication systems require a robust anti-spoofing module as they can be deceived by fabricating spoof images of authorized users. Most recent face anti-spoofing methods rely on optimized architectures and training objectives to alleviate the distribution shift between train and test users. However, in real online scenarios, past data from a user contains valuable information that could be used to alleviate the distribution shift. We thus introduce OAP (Online Adaptive Personalization): a lightweight solution which can adapt the model online using unlabeled data. OAP can be applied on top of most anti-spoofing methods without the need to store original biometric images. Through experimental evaluation on the SiW dataset, we show that OAP improves recognition performance of existing methods on both single video setting and continual setting, where spoof videos are interleaved with live ones to simulate spoofing attacks. We also conduct ablation studies to confirm the design choices for our solution.