Younes Ben Mazziane

Younes Ben Mazziane, Francescomaria Faticanti, Giovanni Neglia et al.

Online learning algorithms have been successfully used to design caching policies with regret guarantees. Existing algorithms assume that the cache knows the exact request sequence, but this may not be feasible in high load and/or memory-constrained scenarios, where the cache may have access only to sampled requests or to approximate requests' counters. In this paper, we propose the Noisy-Follow-the-Perturbed-Leader (NFPL) algorithm, a variant of the classic Follow-the-Perturbed-Leader (FPL) when request estimates are noisy, and we show that the proposed solution has sublinear regret under specific conditions on the requests estimator. The experimental evaluation compares the proposed solution against classic caching policies and validates the proposed approach under both synthetic and real request traces.

Younes Ben Mazziane, Cleque-Marlain Mboulou Moutoubi, Eitan Altman et al.

The Kelly or proportional allocation mechanism is a simple and efficient auction-based scheme that distributes an infinitely divisible resource proportionally to the agents bids. When agents are aware of the allocation rule, their interactions form a game extensively studied in the literature. This paper examines the less explored repeated Kelly game, focusing mainly on utilities that are logarithmic in the allocated resource fraction. We first derive this logarithmic form from fairness-throughput trade-offs in wireless network slicing, and then prove that the induced stage game admits a unique Nash equilibrium NE. For the repeated play, we prove convergence to this NE under three behavioral models: (i) all agents use Online Gradient Descent (OGD), (ii) all agents use Dual Averaging with a quadratic regularizer (DAQ) (a variant of the Follow-the-Regularized leader algorithm), and (iii) all agents play myopic best responses (BR). Our convergence results hold even when agents use personalized learning rates in OGD and DAQ (e.g., tuned to optimize individual regret bounds), and they extend to a broader class of utilities that meet a certain sufficient condition. Finally, we complement our theoretical results with extensive simulations of the repeated Kelly game under several behavioral models, comparing them in terms of convergence speed to the NE, and per-agent time-average utility. The results suggest that BR achieves the fastest convergence and the highest time-average utility, and that convergence to the stage-game NE may fail under heterogeneous update rules.

Younes Ben Mazziane, Vinay Kumar B. R., Othmane Marfoq

\texttt{Elastic-Sketch} is a hash-based data structure for counting item's appearances in a data stream, and it has been empirically shown to achieve a better memory-accuracy trade-off compared to classical methods. This algorithm combines a \textit{heavy block}, which aims to maintain exact counts for a small set of dynamically \textit{elected} items, with a light block that implements \texttt{Count-Min} \texttt{Sketch} (\texttt{CM}) for summarizing the remaining traffic. The heavy block dynamics are governed by a hash function~$β$ that hashes items into~$m_1$ buckets, and an \textit{eviction threshold}~$λ$, which controls how easily an elected item can be replaced. We show that the performance of \texttt{Elastic-Sketch} strongly depends on the stream characteristics and the choice of~$λ$. Since optimal parameter choices depend on unknown stream properties, we analyze \texttt{Elastic-Sketch} under a \textit{stationary random stream} model -- a common assumption that captures the statistical regularities observed in real workloads. Formally, as the stream length goes to infinity, we derive closed-form expressions for the limiting distribution of the counters and the resulting expected counting error. These expressions are efficiently computable, enabling practical grid-based tuning of the heavy and \texttt{CM} blocks memory split (via $m_1$) and the eviction threshold~$λ$. We further characterize the structure of the optimal eviction threshold, substantially reducing the search space and showing how this threshold depends on the arrival distribution. Extensive numerical simulations validate our asymptotic results on finite streams from the Zipf distribution.

Younes Ben Mazziane, Francescomaria Faticanti, Sara Alouf et al.

Online learning algorithms have been successfully used to design caching policies with sublinear regret in the total number of requests, with no statistical assumption about the request sequence. Most existing algorithms involve computationally expensive operations and require knowledge of all past requests. However, this may not be feasible in practical scenarios like caching at a cellular base station. Therefore, we study the caching problem in a more restrictive setting where only a fraction of past requests are observed, and we propose a randomized caching policy with sublinear regret based on the classic online learning algorithm Follow-the-Perturbed-Leader (FPL). Our caching policy is the first to attain the asymptotically optimal regret bound while ensuring asymptotically constant amortized time complexity in the partial observability setting of requests. The experimental evaluation compares the proposed solution against classic caching policies and validates the proposed approach under synthetic and real-world request traces.