In 56, S. Perlaza, A. Jean-Marie and K. Sun studied classical zero-sum games under the following assumptions: $\left(1\right)$ One of the players (the leader) commits to choose its actions by sampling a given probability measure (strategy); $\left(2\right)$ The leader announces its action, which is observed by its opponent (the follower) through a binary channel; and $\left(3\right)$ the follower chooses its strategy based on the knowledge of the leader's strategy and the noisy observation of the leader's action. Under these conditions, the equilibrium is shown to always exist. Interestingly, even subject to noise, observing the actions of the leader is shown to be either beneficial or immaterial for the follower. More specifically, the payoff at the equilibrium of this game is upper bounded by the payoff at the Stackelberg equilibrium (SE) in pure strategies; and lower bounded by the payoff at the Nash equilibrium, which is equivalent to the SE in mixed strategies. Finally, necessary and sufficient conditions for observing the payoff at equilibrium to be equal to its lower bound are presented. Sufficient conditions for the payoff at equilibrium to be equal to its upper bound are also presented. This work was presented as a conference in 41.

S. Perlaza, A. Jean-Marie, and E. Athanasakos are currently extending these results to more general classes of channels. In particular, Gaussian channels.

In 54, E. Altman, S. Perlaza, and A. Krishnan K.S. considered different pricing models for a platform-based rental system, such as Airbnb. A linear model is assumed for the demand response to price, and existence and uniqueness conditions for Nash equilibria are obtained. The Stackelberg equilibrium prices for the game are also obtained, and an iterative scheme is provided, which converges to the Nash equilibrium. Different cooperative pricing schemes are studied, and splitting of revenues based on the Shapley value is discussed. It is shown that a division of revenue based on the Shapley value gives a revenue to the platform proportional to its control of the market. The demand response function is modified to include user response to quality of service. It is shown that when the cost to provide quality of service is low, both renter and the platform will agree to maximize the quality of service. However, if this cost is high, they may not always be able to agree on what quality of service to provide. This work was presented as a conference in 32.

In 42 R. Taisant (INOCS), M. Datar, H. Le Cadre (INOCS), and E. Altman consider a peer-to-peer electricity market modeled as a network game, where End Users (EUs) minimize their cost by computing their demand and generation while satisfying a set of local and coupling constraints. The nominal demand of EUs constitutes sensitive information, that EUs might want to keep private. The authors of 42 prove that the network game admits a unique Variational Equilibrium, which depends on the private information of all the EUs. A data aggregator is introduced, which aims to learn the EUs’ private information. The EUs might have incentives to report biased and noisy readings to preserve their privacy, which creates shifts in their strategies. Relying on performative prediction, the authors define a decision-dependent game G${}^{\mathrm{stoch}}$ to couple the network game with a data market. Two variants of the Repeated Stochastic Gradient Method (RSGM) are proposed to compute the Performatively Stable Equilibrium solution of G${}^{\mathrm{stoch}}$, that outperform RSGM with respect to efficiency gap minimization, privacy preservation, and convergence rates in numerical simulations. This work has been extended in 55 by H. Le Cadre and M. Guckert (INOCS), M. Datar and E. Altman (also LIA).

In 13 K. Avrachenkov in collaboration with E. Morozov and R. Nekrasova (Karelian Institute of Applied Mathematical Research, Russia) establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. They also characterize an interesting phenomenon of partial stability when one orbit is tight but the other orbit goes to infinity in probability. All theoretical results are illustrated by numerical experiments.

Motivated primarily by electric vehicles (EV) queueing at charging stations, B.R. Vinay Kumar studies multiple server queues on an Euclidean space. He considers $N$ servers that are distributed uniformly in ${[0,1]}^d$. Customers or EV users arrive at the servers according to Poisson processes of intensity $\lambda$. However, they probabilistically decide whether to join the queue they arrived at, or move to one of the nearest neighbors. The strategy followed by the customers affects the load on the servers in the long run. In 43, 57, B.R. Vinay Kumar is interested in characterizing the fraction of servers that bear a larger load as compared to when the users do not follow any strategy, i.e., they join the queue at which they arrive. These are called overloaded servers. He evaluates the expected fraction of overloaded servers in the system for the one dimensional case ($d=1$) when the users follow probabilistic nearest neighbor shift strategies.

Similarity caching allows requests for an item to be served by a similar item. Applications include recommendation systems, multimedia retrieval, and machine learning. Recently, many similarity caching policies have been proposed, like SIM-LRU (Similarity Least Recently Used) and its generalization RND-LRU (Random Least Recently Used), but the performance analysis of their hit ratio is still wanting. Y. Ben Mazziane, S. Alouf, and G. Neglia, together with D. S. Menasche (Federal Univ. of Rio de Janeiro, Brazil) are pursuing their effort to estimate the hit ratio of the similarity caching policy RND-LRU. They extend the popular time-to-live approximation in classic caching to similarity caching. They introduce the RND-TTL (Random Time-to-Live) approximation and the RND-TTL cache model and tune the model's parameters in such a way as to mimic the behavior of RND-LRU. The parameter tuning involves solving a fixed point system of equations for which they provide an algorithm for numerical resolution and sufficient conditions for its convergence.

In 17, R. Dhounchak and V. Kavitha (IIT Mumbai) in collaboration with E. Altman consider the inherent timeline structure of the appearance of content in online social networks (OSNs) while studying content propagation. They model the propagation of a post/content of interest by a multi-type branching process. The latter allows one to predict the emergence of global macro properties (e.g., the spread of a post in the network) from the laws and parameters that determine local interactions. The local interactions largely depend upon the timeline (an inverse stack capable of holding many posts and one dedicated to each user) structure and the number of friends (i.e., connections) of users, etc. They explore the use of multi-type branching processes to analyze the viral properties of the post, e.g., to derive the expected number of shares, the probability of virality of the content, etc. In OSNs, the new posts push down the existing contents in timelines, which can greatly influence content propagation; their analysis considers this influence. They find that one leads to draw incorrect conclusions when the timeline (TL) structure is ignored. One cannot capture some interesting paradigm shifts/phase transitions; for example, virality chances are not monotone with network activity parameter, as shown by analysis including TL influence.

Classical problems such as classification, pattern recognition, regression, and density estimation can be posed as special cases of the ERM problem. Unfortunately, ERM is prone to training data memorization, a phenomenon also known as overfitting. For this reason, ERM is often regularized in order to provide generalization guarantees. That is, to identify models using available training datasets that induce low empirical risk with respect to unseen datasets. At Neo  special attention is payed to the study of the statistical properties of the solutions to ERM problems subject to particular regularizations. The main feature of this research effort is that contrary to the main stream in the community, this analysis is made for fixed training datasets, which provides new and insightful mathematical tools for the analysis of generalization capabilities of machine learning algorithms.

The expected generalization error (GE) is a central performance metric for the analysis of generalization capabilities of machine learning algorithms. In a nutshell, the GE characterizes the ability of a learning algorithm to correctly find patterns in datasets that are not available during the training stage. Specifically, it is defined for a fixed training dataset and a specific model instance, as the difference between the population risk induced by the model and the empirical risk with respect to the training dataset. At Neo  our research focuses on the search of closed-form expressions of the GE for specific algorithms under the assumption that datasets follow a specific probability distribution that is consistent with the training dataset.

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 27, Y. Ben Mazziane, F. Faticanti, G. Neglia, and S. Alouf 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 they 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.

In 29, F. Faticanti and G. Neglia study a batched version of optimistic online algorithms for caching. The analysis consists of updating the cache state less frequently with respect to traditional caching algorithms that update the cache state after receiving every single new request. This new approach proposes to cumulate a batch of requests before updating the cache given the high computational complexity of online algorithms based on Follow-The-Regularized-Leader (FTRL). No-regret results are showed in this new setting and experimental results show that the batched versions of the online algorithms outperform traditional caching policies on both synthetic and real traces.

The abstract of the paper “Enabling Long-term Fairness in Dynamic Resource Allocation ” has been published in the Proceedings of the 2023 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems 40. The corresponding research activity is described in NEO activity report for 2022.

In 35 K. Avrachenkov in collaboration with T. Pagare and V. Borkar (IIT Bombay, India) extend the provably convergent Full Gradient DQN (Deep Q-Network) algorithm for discounted reward Markov decision processes from Avrachenkov et al. (2021) to average reward problems. They experimentally compare widely used RVI (Relative Value Iteration) Q-learning with recently proposed Differential Q-learning in the neural function approximation setting with Full Gradient DQN and DQN. They also extend this to learn Whittle indices for Markovian restless multi-armed bandits and observe a better convergence rate of the proposed Full Gradient variant across different tasks.

K. Avrachenkov in collaboration with V. Borkar and J. Nair (IIT Bombay, India) have organized and edited a special volume of Dynamic Games and Applications journal on the topic “Multi-Agent Dynamic Decision Making and Learning” 45. This field interests multiple communities such as dynamic games, control theory and machine learning, especially, reinforcement learning. 14 papers have been accepted and published in this special volume.

In 37, A. Rodio, F. Faticanti, O. Marfoq, and G. Neglia in collaboration with E. Leonardi (Polytechnic Univ. of Turin, Italy) provide the first convergence result for Federated Learning algorithms under heterogeneous and correlated client availability. Their analysis shows the negative impact of correlation on the algorithms' convergence rate and highlights a trade-off between optimization error (related to convergence speed) and bias error (indicative of model quality). Their proposed Correlation-Aware FL (CA-Fed) algorithm effectively balances convergence speed and model quality by adjusting client aggregation weights and selectively excluding highly correlated, low-availability clients. Throughout simulations, CA-Fed achieves higher time-average accuracy and reduced standard deviation compared to existing methods on both synthetic and real datasets.

Subsequently, in 21, A. Rodio, F. Faticanti, O. Marfoq, and G. Neglia in collaboration with E. Leonardi (Polytechnic Univ. of Turin, Italy) further enhance their CA-Fed algorithm by introducing a new hyper-parameter to optimize the trade-off between convergence speed and model quality. A sensitivity analysis confirms this parameter's impact on convergence. In contrast to 37, which relied on prior knowledge of clients' availability and correlation, they propose a Bayesian estimator with a beta prior, requiring only a limited amount of observations to outperform existing methods. Additionally, they address a gap in 37 by evaluating CA-Fed in spatially correlated scenarios, where the availability patterns are correlated among clients.

In 38, A. Rodio and G. Neglia in collaboration with F. Busacca and S. Palazzo (Univ. of Catania, Italy), S. Mangione and I. Tinnirello (Univ. of Palermo, Italy), and F. Restuccia (Northeastern Univ., USA) address training Federated Learning algorithms in wireless networks with packet losses. Contrary to conventional approaches that focus on mitigating packet losses through retransmission or error correction, they show that FL algorithms can effectively learn in asymmetric lossy channels while maintaining the same computational and communication efficiency. Their proposed algorithm, UPGA-PL (Unbiased Pseudo-Gradient Aggregation with Packet Losses), employs a pseudo-gradient step rather than model averaging, and adjusts the aggregation weights for heterogeneous packet losses. In experimental evaluation, UPGA-PL outperforms existing methods in lossy environments and matches Federated Learning algorithms in lossless scenarios within a limited number of communication rounds.

Most work on federated learning assumes that clients operate on static datasets collected before training starts. This approach may be inefficient because 1) it ignores new samples clients collect during training, and 2) it may require a potentially long preparatory phase for clients to collect enough data. Moreover, learning on static datasets may be simply impossible in scenarios with small aggregate storage across devices. It is, therefore, necessary to design federated algorithms able to learn from data streams. In 34 O. Marfoq and G. Neglia, together with L. Kameni and R. Vidal from (Accenture Labs, France) formulate and study the problem of federated learning for data streams. They propose a general FL algorithm to learn from data streams through an opportune weighted empirical risk minimization. Their theoretical analysis provides insights to configure such an algorithm, and they evaluate its performance on a wide range of machine learning tasks.

In 39, C. Kaplan in collaboration with A.S. de Oliveira (SAP Labs France), Khawla Mallat (SAP Labs France), and Tanmay Chakraborty (SAP Labs France, Eurecom) investigate the impact of differential privacy on fairness notions for tabular data. They empirically analyze how different fairness notions, belonging to distinct classes of statistical fairness criteria, are impacted when one selects a model architecture suitable for DP-SGD (differentially private stochastic gradient descent), optimized for utility. Using standard datasets from ML fairness literature, they show that by selecting the optimal model architecture for DP-SGD, the differences across groups concerning the relevant fairness metrics more often decrease or are negatively impacted, compared to the non-private baseline, for which the optimal model architecture has also been selected to maximize utility. These findings challenge the understanding that differential privacy will necessarily exacerbate unfairness in deep learning models trained on biased datasets.

Since 2020, S. Perlaza in collaboration with X. Ye, I. Esnaola, and R. Harrison (Univ. of Sheffield) have studied sparse stealth attack constructions that minimize the mutual information between the state variables and the observations. In 25, the attack construction is formulated as the design of a multivariate Gaussian distribution that aims to minimize the mutual information while limiting the Kullback-Leibler divergence between the distribution of the observations under attack and the distribution of the observations without attack. The sparsity constraint is incorporated as a support constraint of the attack distribution. Two heuristic greedy algorithms for the attack construction are proposed. The first algorithm assumes that the attack vector consists of independent entries, and therefore, requires no communication between different attacked locations. The second algorithm considers correlation between the attack vector entries and achieves a better disruption to stealth tradeoff at the cost of requiring communication between different locations. Numerical evaluations show that it is feasible to construct stealth attacks that generate significant disruption with a low number of compromised sensors.

In 26 K. Avrachenkov and B.R. Vinay Kumar in collaboration with K. Alaluusua and L. Leskelä (Aalto University, Finland) consider the community recovery problem on a multilayer variant of the hypergraph stochastic block model (HSBM). Each layer is associated with an independent realization of a $d$-uniform HSBM on $N$ vertices. Given the similarity matrix containing the aggregated number of hyperedges incident to each pair of vertices, the goal is to obtain a partition of the $N$ vertices into disjoint communities. In this work, they investigate a semidefinite programming (SDP) approach and obtain information-theoretic conditions on the model parameters that guarantee exact recovery both in the assortative and the disassortative cases.

In 31, 60 K. Avrachenkov and L. Hauseux in collaboration with J. Zerubia (Ayana team) propose an original density estimator built from a cloud of points $X\in R^d$. To do this, they consider geometric graphs $G(X,r)$ on the cloud. These graphs depend on a radius $r$. By varying the radius, they see the emergence of large components around certain critical radii, which is the phenomenon of continuum percolation. Percolation allows us to have both a local view of the data (through local constraints on the radius $r$) and a global one (the emergence of macro-structures). With this tool, they address the problem of galaxy filament extraction. The density estimator gives us a relevant graph on galaxies. With an algorithm sharing the ideas of the Fréchet mean, they extract a subgraph from this graph, the galaxy filaments.

In 33 Vijith Kumar K. P. together with B. Kumar Rai and T. Jacob (IIT Guwahati, India) consider the $(N,K,L)$ multi-access caching network where $K$ users and $K$ caches are connected to a server with $N$ files, each of size $F$ bits, through a shared error-free broadcast channel. Each user has access to $L$ nearby caches, each of size $MF$ bits, in a cyclic wrap-around manner. Even after several previous attempts, the exact characterization of the optimal rate memory tradeoff is still an open problem except in the case where $L=K-1$ and $L=1$ with large cache $M\in [N/L·(K-1)/K,N/L]$. This paper determines the optimal rate memory tradeoff for the cache network with $L=K-2$ and $M\in [N/(K-2)·(K-1)/K,N/(K-2\left)\right]$. This is done by proposing a new caching scheme that operates at the memory rate pair $(N/(K-2)·(K-1)/K,1/K)$ and deriving a set of lower bounds to demonstrate the optimality of the scheme.

In 18 F. Faticanti in collaboration with M. Savi (Univ. Milano-Bicocca, Italy), F. De Pellegrini (Univ. Avignon) and D. Siracusa (Fondazione Bruno Kessler, Italy) propose a new approach for the deployment of microservice-based applications in a Federated Fog Computing scenario under locality constraints for a subset of microservices of the application. The approach is based on a Breadth-First-Search (BFS) visit of the search space for the deployment of applications where the main objective is to minimize the deployment cost towards external fog domains with respect to the main provider. Experiments show that the proposed approach outperforms traditional deployment methods based on Depth-First-Search visits of the search space.

Modern portable devices can execute increasingly sophisticated AI models on sensed data. The complexity of such processing tasks is data-dependent and has relevant energy cost. In 30, A. Fox, F. De Pellegrini (Univ. Avignon) and E. Altman develop an Age of Information Markovian model for a system where multiple battery-operated devices perform data processing and energy harvesting in parallel. Part of their computational burden is offloaded to an edge server which polls devices at a given rate. The structural properties of the optimal policy for a single device-server system are derived. They permit to derive a new model-free reinforcement learning method specialized for monotone policies, namely Ordered Q-Learning, providing a fast procedure to learn the optimal policy. The method is oblivious to the devices’ battery capacities, the cost and the value of data batch processing and to the dynamics of the energy harvesting process. Finally, the polling strategy of the server is optimized by combining such policy improvement techniques with stochastic approximation methods. Extensive numerical results provide insight into the system properties and demonstrate that the proposed learning algorithms outperform existing baselines.

We have been extending our research on games in networks where users compete over resources, to the case in which competition arises also between the users and the supplier of services and further to the case when the suppliers compete between each other through the prices of their services. This bundelling of services called Network slicing (NS) is a key technology in 5G that enables the customization and efficient sharing of network resources to support the diverse requirements of next-generation services.

In 15, M. Datar, E. Altman and H. Le Cadre (INOCS) consider a marketplace in the context of 5G network slicing, where Application Service Providers (ASP), i.e., slice tenants, providing heterogeneous services, are in competition for the access to the virtualized network resource owned by a Network Slice Provider (NSP), who relies on network slicing. They model the interactions between the end users (followers) and the ASPs (leaders) as a Stackelberg game. They prove that the competition between the ASPs results in a multi-resource Tullock rent-seeking game. To determine resource pricing and allocation, They devise two innovative market mechanisms.

In 16, S. Dhamal, W. Ben-Ameur, and T. Chahed (Télécom SudParis), E. Altman, A. Sunny (ITT Palakkad), and S. Poojary (Qualcomm India) study a distributed computing setting wherein a central entity seeks power from computational providers by offering a certain reward in return. The computational providers are classified into long-term stakeholders that invest a constant amount of power over time and players that can strategize on their computational investment. In this paper, they model and analyze a stochastic game where players arrive and depart over time. They prove that, in Markov perfect equilibrium, only players with cost parameters in a relatively low range which collectively satisfy a certain constraint in a given state, invest. They infer that players need not have knowledge about the system state and other players’ parameters, if the total power that is being received by the central entity is communicated to the players as part of the system’s protocol. If players are homogeneous and the system consists of a reasonably large number of players, They observe that the total power received by the central entity is proportional to the offered reward and does not vary significantly despite the players’ arrivals and departures, thus resulting in a robust and reliable system. They study by simulations and mean field approximation, how the players’ utilities are influenced by the system parameters.

In 51, M. Datar (currently at Orange Innovation), N. Modina (CNAM), R. El Azouzi (Univ. Avignon), and E. Altman propose an allocation scheme for network slicing based on the Fisher-market model and the Trading-post mechanism. The scheme aims to achieve efficient resource utilization while ensuring multi-level fairness, dynamic load conditions, and the protection of service level agreements (SLAs) for slice tenants. In the proposed scheme, each service provider (SP) is allocated a budget representing its infrastructure share or purchasing power in the market.