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arXiv · 2101.12588

No-Regret Caching via Online Mirror Descent

T. Si Salem·G. Neglia·S. Ioannidis
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Abstract

We study an online caching problem in which requests can be served by a local cache to avoid retrieval costs from a remote server. The cache can update its state after a batch of requests and store an arbitrarily small fraction of each file. We study no-regret algorithms based on Online Mirror Descent (OMD) strategies. We show that bounds for the regret crucially depend on the diversity of the request process, provided by the diversity ratio R/h, where R is the size of the batch, and h is the maximum multiplicity of a request in a given batch. We characterize the optimality of OMD caching policies w.r.t. regret under different diversity regimes. We also prove that, when the cache must store the entire file, rather than a fraction, OMD strategies can be coupled with a randomized rounding scheme that preserves regret guarantees, even when update costs cannot be neglected. We provide a formal characterization of the rounding problem through optimal transport theory, and moreover we propose a computationally efficient randomized rounding scheme.

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T. Si Salem, G. Neglia, S. Ioannidis. 2021-01-29. No-Regret Caching via Online Mirror Descent. https://arxiv.org/abs/2101.12588

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