Learning to Cache With No Regrets

Abstract

This paper introduces a novel caching analysis that, contrary to prior work, makes no modeling assumptions for the file request sequence. We cast the caching problem in the framework of Online Linear Optimization (OLO), and introduce a class of minimum regret caching policies, which minimize the losses with respect to the best static configuration in hindsight when the request model is unknown. These policies are very important since they are robust to popularity deviations in the sense that they learn to adjust their caching decisions when the popularity model changes. We first prove a novel lower bound for the regret of any caching policy, improving existing OLO bounds for our setting. Then we show that the Online Gradient Ascent (OGA) policy guarantees a regret that matches the lower bound, hence it is universally optimal. Finally, we shift our attention to a network of caches arranged to form a bipartite graph, and show that the Bipartite Subgradient Algorithm (BSA) has no regret.

Online Convex Optimization for Caching Networks

“…We assume that file requests are drawn from a general distribution, which is equivalent to caching versus an adversary that chooses the requests arbitrarily. 1 At each slot (i) the adversary creates a new file request; (ii) a routing plan is deployed to retrieve the file from the SBS caches and/or MBS; (iii) a (file, cache)-dependent utility is obtained; and (iv) the caching policy updates the stored files at each SBS. This generalizes the criterion of cache hit ratio and allows one to build policies that, for instance, minimize delay or provide different priority to different users.…”

“…George Iosifidis is with the School of Computer Science and Statistics, Trinity College Dublin, The University of Dublin, College Green, Dublin 2, D02PN40 Ireland (e-mail: george.iosifidis@tcd.ie). Part of this work has appeared in the proceedings of IEEE INFOCOM 2019 [1]. The work of G. Iosifidis is supported by the Science Foundation Ireland under Grants 17/CDA/4760 and 16/IA/4610.…”

“…The first OCO-based caching policy was proposed in [1] which reformulated the caching problem and embedded a learning mechanism, while [27] studied how such policies can be used in device-to-device caching scenarios. In CNs one needs to additionally decide which cache will satisfy a request (routing) and which files will be evicted (caching), and these decisions are perplexed when each user is connected to multiple caches.…”

“…Following the rationale of the analysis in [5], we show that our policy achieves no regret and we analyze how the various system parameters affect the regret expression. R T (BSCA) ≤ w (1) 2degJCT , where C = max j C j , deg= max i∈I |J i |, w (1) = max n,i,j w n,i,j Proof: Using the non-expansiveness property of the Euclidean projection [39], we can bound the distance of each new value y t+1 from the hindsight policy y * , as follows:…”

“…Project: y t+1 = Π Y (q t+1 ); % decides caching end the specific file. Further, its smallest value is zero by the nonnegativity of Lagrangian multipliers, and its largest is no more than the maximum utility, denoted with w (1) . Thus, using deg = max i∈I |J i | we can bound the supergradient norm:…”