Caching in Networks without Regret
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by
Debjit Paria, Krishnakumar, Abhishek Sinha
2020
Abstract
We consider the online Bipartite Caching problem where n users
are connected to m caches in the form of a bipartite network. Each of the m
caches has a file storage capacity of C. There is a library consisting of N
>C distinct files. Each user can request any one of the files from the library
at each time slot. We allow the file request sequences to be chosen in an
adversarial fashion. A user's request at a time slot is satisfied if the
requested file is already hosted on at least one of the caches connected to the
user at that time slot. Our objective is to design an efficient online caching
policy with minimal regret. In this paper, we propose LeadCache, an
online caching policy based on the Follow the Perturbed Leader
(FTPL) paradigm. We show that LeadCache is regret optimal up to a
multiplicative factor of Õ(n^0.375). As a byproduct of our
analysis, we design a new linear-time deterministic Pipage rounding procedure
for the LP relaxation of a well-known NP-hard combinatorial optimization
problem in this area. Our new rounding algorithm substantially improves upon
the currently best-known complexity for this problem. Moreover, we show the
surprising result that under mild Strong-Law-type assumptions on the file
request sequence, the rate of file fetches to the caches approaches to zero
under the LeadCache policy. Finally, we derive a tight universal
regret lower bound for the Bipartite Caching problem, which
critically makes use of results from graph coloring theory and certifies the
announced approximation ratio.
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