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TopRank-Based Delivery Rate Optimization for Coded Caching under Non-Uniform Demands

Mohammadsaber Bahadori, Seyed Pooya Shariatpanahi, Behnam Bahrak

TL;DR

This work proposes a method inspired by an algorithm from the recommender-systems literature and multi-armed bandits that achieves significantly improved performance in scenarios where the number of users in the network is small, the cache storage capacity is limited, or the learning process of the true popularity of files based on observations is contaminated by exploratory or synthetic requests that do not match the true popularity distribution.

Abstract

We study the problem of coded caching with nonuniform file popularity under the setting where the popularity distribution is initially unknown. By reframing the problem, we propose a method inspired by an algorithm from the recommender-systems literature and multi-armed bandits. Unlike prior approaches, which focus on accurately estimating file popularities, our method ranks files relative to one another and partitions them into groups. This perspective is more consistent with the structure of prior approaches as well, since earlier methods also divided files into popular and non-popular groups after estimating their popularities. The proposed approach relies on differences in request counts between files as the basis for ranking, and under many conditions it outperforms the previous algorithm. In particular, we obtain significantly improved performance in scenarios where the number of users in the network is small, the cache storage capacity is limited, or the learning process of the true popularity of files based on observations is contaminated by exploratory or synthetic requests that do not match the true popularity distribution. In these cases, our policy achieves markedly better performance and attains sublinear regret.

TopRank-Based Delivery Rate Optimization for Coded Caching under Non-Uniform Demands

TL;DR

This work proposes a method inspired by an algorithm from the recommender-systems literature and multi-armed bandits that achieves significantly improved performance in scenarios where the number of users in the network is small, the cache storage capacity is limited, or the learning process of the true popularity of files based on observations is contaminated by exploratory or synthetic requests that do not match the true popularity distribution.

Abstract

We study the problem of coded caching with nonuniform file popularity under the setting where the popularity distribution is initially unknown. By reframing the problem, we propose a method inspired by an algorithm from the recommender-systems literature and multi-armed bandits. Unlike prior approaches, which focus on accurately estimating file popularities, our method ranks files relative to one another and partitions them into groups. This perspective is more consistent with the structure of prior approaches as well, since earlier methods also divided files into popular and non-popular groups after estimating their popularities. The proposed approach relies on differences in request counts between files as the basis for ranking, and under many conditions it outperforms the previous algorithm. In particular, we obtain significantly improved performance in scenarios where the number of users in the network is small, the cache storage capacity is limited, or the learning process of the true popularity of files based on observations is contaminated by exploratory or synthetic requests that do not match the true popularity distribution. In these cases, our policy achieves markedly better performance and attains sublinear regret.
Paper Structure (12 sections, 2 theorems, 19 equations, 4 figures, 1 algorithm)

This paper contains 12 sections, 2 theorems, 19 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. PROBLEM SETTING
  3. System Model
  4. Decentralized Coded Caching
  5. Online Learning
  6. Proposed Policy
  7. Oracle Policy
  8. Numerical Experiment
  9. Proof of Lemma \ref{['increaseN_2']}
  10. Proof of Lemma \ref{['stepsneed']}
  11. Example for determining the popular group in the oracle policy
  12. Additional Simulation Notes

Key Result

Lemma 4.1

To determine the popular group under the oracle policy, increasing the size of the popular group without adding any new requested files only increases the rate unnecessarily. Intuitively, as the size of the popular group grows, $N^t_2$ increases, while the number of bits stored per file ($\frac{M}{N

Figures (4)

  • Figure 1: Network Model
  • Figure 2: Regret comparison between our proposed policy (OPM1 and OPM2) and the policy in TopRank (NSK) under different network settings. The 'NSK' curve continues its approximately linear growth even beyond the domain displayed in the plots.
  • Figure 3: $K=100$ , $M = 10$ , Size of the popular group in different algorithms for a system with parameters $K=100$ and $M = 10$.
  • Figure 4: The sizes of different partitions over time in the 3,000-user system with $\delta=1/(nK)$. This number of users was chosen so that significant changes could be observed within a small time window.

Theorems & Definitions (2)

  • Lemma 4.1
  • Lemma 4.2