Online Caching Networks with Adversarial Guarantees

Abstract

We study a cache network under arbitrary adversarial request arrivals. We propose a distributed online policy based on the online tabular greedy algorithm [4]. Our distributed policy achieves sublinear (1 − 1 𝑒 )-regret, also in the case when update costs cannot be neglected. Numerical evaluation over several topologies supports our theoretical results and demonstrates that our algorithm outperforms state-of-art online cache algorithms.

Optimistic No-regret Algorithms for Discrete Caching

“…For instance, requests in services like Facebook are often amenable to accurate forecasts; while in YouTube and Netflix the viewers receive recommendations which can effectively serve as predictions for their forthcoming requests [20], [21]. Unfortunately, regretbased caching policies, such as [14], [13], [12], [11], [16], [22], are pessimistically designed for the worst-case request sequence and cannot benefit from predictable requests. We tackle this shortcoming by designing a new suite of optimistic caching algorithms.…”

“…A large body of works focus on offline policies which use the anticipated request pattern to proactively populate the caches with files that maximize the expected hits [1]. At the other extreme, dynamic caching solutions studied variants of the LFU/LRU policies [6], [7], [30], [31]; track the request distribution [32], [33] and optimize accordingly the caching [34]; employed reinforcement learning to adapt the caching decisions to requests [35], [36], [37]; and, more recently, applied online convex optimization towards enabling the policies to handle unknown (adversarial) request patterns [14], [12], [15], [11], [16], [13], [22]. These latter works assume that the files can be fetched dynamically at each slot to optimize the cache configuration, as opposed to works such as [26], [27] which study pure eviction policies.…”

“…Their approach was generalized to metrical task systems by [41] and improved with nearly lower-bound matching for the competitive ratios in [42]. However, as proved in [43], algorithms that ensure constant competitive-ratios do not necessarily guarantee sub-linear regret, which is the performance criterion we employ here following the recent regret-based caching research [14], [12], [15], [11], [16], [13], [22]. We note that all above works consider files with equal size, while we extend the framework to the general scenario of unequally-sized files.…”

“…T ( [22] uses the standard doubling trick) and use the Lipschitz constant for the gradient (i.e., request) vector. Thus, they are not classified as performing Adaptive Learning (Adap.…”

“…where inequality (a) follows from the 1 /2-approximation property of the randomized rounding algorithm (22); and (b) follows from the result of Theorem 2. In fact, that theorem operates on integral decisions x t , yet we can recall that x is integral and that we showed E [x t ] = xt ; thus, the same guarantee can be used here.…”