An Online Gradient-Based Caching Policy with Logarithmic Complexity and Regret Guarantees

The commonly used caching policies, such as LRU or LFU, exhibit optimal performance only for specific traffic patterns. Even advanced Machine Learning-based methods, which detect patterns in historical request data, struggle when future requests deviate from past trends. Recently, a new class of policies has emerged that makes no assumptions about the request arrival process. These algorithms solve an online optimization problem, enabling continuous adaptation to the context. They offer theoretical guarantees on the regret metric, which is the gap between the gain of the online policy and the gain of the optimal static cache allocation in hindsight. Nevertheless, the high computational complexity of these solutions hinders their practical adoption. In this study, we introduce a groundbreaking gradient-based online caching policy, the first to achieve logarithmic computational complexity relative to catalog size along with regret guarantees. This means our algorithm can efficiently handle large-scale data while minimizing the performance gap between real-time decisions and optimal hindsight choices. As requests arrive, our policy dynamically adjusts the probabilities of including items in the cache, which drive cache update decisions. Our algorithm's streamlined complexity is a key advantage, enabling its application to real-world traces featuring millions of requests and items. This is a significant achievement, as traces of this scale have been out of reach for existing policies with regret guarantees. To the best of our knowledge, our experimental results show for the first time that the regret guarantees of gradient-based caching policies bring significant benefits in scenarios of practical interest.