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Journal Articles ACM Transactions on Modeling and Performance Evaluation of Computing Systems Year : 2023

No-regret Caching via Online Mirror Descent

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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Dates and versions

hal-04181387 , version 1 (15-08-2023)

Identifiers

Cite

Tareq Si Salem, Giovanni Neglia, Stratis Ioannidis. No-regret Caching via Online Mirror Descent. ACM Transactions on Modeling and Performance Evaluation of Computing Systems, 2023, 8 (4), pp.1-32. ⟨10.1145/3605209⟩. ⟨hal-04181387⟩
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