Generalization Bounds for Time Series Prediction with Non-stationary Processes

GLOBECOM 2017 - 2017 IEEE Global Communications Conference

Nagananda

Guenduez³

et al. 2017

Content caching at the small-cell base stations (sBSs) of a heterogeneous wireless network is considered. A cost function is proposed that captures the backhaul link load called the "offloading loss", which measures the fraction of the requested files that are not available in the sBS caches. Previous approaches in the literature minimize this offloading loss assuming that the popularity profile of the cached content is time-invariant and perfectly known. However, in many practical applications, the popularity profile is unknown and time-varying. Therefore, the analysis of caching with non-stationary and statistically dependent popularity profiles (assumed unknown, and hence, estimated) is studied in this paper from a learningtheoretic perspective. A probably approximately correct result is derived, in which a high probability bound on the offloading loss difference, i.e., the error between the estimated and the optimal offloading loss, is investigated. The difference is a function of the Rademacher complexity of the set of all probability measures on the set of cached content items, β−mixing coefficient, 1/ √ t (t is the number of time slots), and a measure of discrepancy between the estimated and true popularity profiles.

Section: Appendix a Proof Of Theoremmentioning

confidence: 95%

“…For example, if ∆ T (t, T ) is small, then each term in (3) is small, and therefore results in a small average error. This approach is used in analyzing problems involving non-stationary stochastic processes [14].…”

Section: Problem Statementmentioning

confidence: 99%

Learning-Based Content Caching with Time-Varying Popularity Profiles

GLOBECOM 2017 - 2017 IEEE Global Communications Conference

Nagananda

Guenduez³

et al. 2017

“…For example, if ∆ T (t, T ) is small, then each term in (3) is small, which results in a small average offloading loss. This approach is central to the analyses of prediction problems involving nonstationary stochastic processes [33].…”

Section: Problem Statementmentioning

confidence: 99%

Caching With Time-Varying Popularity Profiles: A Learning-Theoretic Perspective

Nagananda

Gündüz

et al. 2018

IEEE Trans. Commun.

Content caching at the small-cell base stations (sBSs) in a heterogeneous wireless network is considered. A cost function is proposed that captures the backhaul link load called the "offloading loss", which measures the fraction of the requested files that are not available in the sBS caches.As opposed to the previous approaches that consider time-invariant and perfectly known popularity profile, caching with non-stationary and statistically dependent popularity profiles (assumed unknown, and hence, estimated) is studied from a learning-theoretic perspective. A probably approximately correct result is derived, which presents a high probability bound on the offloading loss difference, i.e., the error between the estimated and the optimal offloading loss. The difference is a function of the Rademacher complexity, the β−mixing coefficient, the number of time slots, and a measure of discrepancy between the estimated and true popularity profiles. A cache update algorithm is proposed, and simulation results are presented to show its superiority over periodic updates. The performance analyses for Bernoulli and Poisson request models are also presented. Index TermsCaching; time-varying popularity profiles; probably approximately correct (PAC) learning.

“…, K. In the above, (a) follows from the fact that the convex combination of the terms being greater than a constant implies that at least one of the term should be greater than the constant, and using the union bound. The inequality (b) is obtained by applying proposition 1 of [21] to the indicator function g 1{∆Ψ k,i,t > ǫ t,k } with expectation replaced by the conditional expectation E * | E c [αt:t] . Recall that the event E δ,τ corresponds to the error in decoding the correct index i * at time τ in Step 1 of the algorithm, and E [αt:t] = t τ =αt E δ,τ .…”

Section: Appendix C Proof Of Theoremmentioning

confidence: 99%

Time complexity analysis of distributed stochastic optimization in a non-stationary environment

2017 15th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

Vaishali

2017

In this paper, we consider a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of related stochastic processes called penalties. We assume that the state of the system is evolving in an independent and non-stationary fashion and the "common information" available at each node is distributed and delayed. Such stochastic optimization is an integral part of many important problems in wireless networks such as scheduling, routing, resource allocation and crowd sensing. We propose an approximate distributed Drift-Plus-Penalty (DPP) algorithm, and show that it achieves a time average cost (and penalties) that is within ǫ > 0 of the optimal cost (and constraints) with high probability. Also, we provide a condition on the convergence time t for this result to hold. In particular, for any delay D ≥ 0 in the common information, we use a coupling argument to prove that the proposed algorithm converges almost surely to the optimal solution. We use an application from wireless sensor network to corroborate our theoretical findings through simulation results.