Foundation Models (FMs) have become the hallmark of modern AI, however, these models are trained on massive data, leading to financially expensive training. Updating FMs as new data becomes available is important, however, can lead to `catastrophic forgetting', where models underperform on tasks related to data sub-populations observed too long ago. This continual learning (CL) phenomenon has been extensively studied, but primarily in a setting where only a small amount of past data can be stored. We advocate for the paradigm where memory is abundant, allowing us to keep all previous data, but computational resources are limited. In this setting, traditional replay-based CL approaches are outperformed by a simple baseline which replays past data selected uniformly at random, indicating that this setting necessitates a new approach. We address this by introducing a framework of adaptive memory replay for continual learning, where sampling of past data is phrased as a multi-armed bandit problem. We utilize Bolzmann sampling to derive a method which dynamically selects past data for training conditioned on the current task, assuming full data access and emphasizing training efficiency. Through extensive evaluations on both vision and language pre-training tasks, we demonstrate the effectiveness of our approach, which maintains high performance while reducing forgetting by up to 10% at no training efficiency cost.
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