## About

350

Publications

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5,339

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Introduction

K. E. Avrachenkov currently works at the NEO team - Stochastic Operations Research and Network Science, at INRIA (National Institute for Research in Computer Science and Control). K. E. Avrachenkov does research in Control Systems Engineering, Networks, Machine Learning and Probability Theory.

Additional affiliations

October 2000 - present

Education

April 2009 - April 2010

March 1996 - August 1999

September 1990 - February 1996

## Publications

Publications (350)

This book is a general introduction to the statistical analysis of networks, and can serve both as a research monograph and as a textbook. Numerous fundamental tools and concepts needed for the analysis of networks are presented, such as network modeling, community detection, graph-based semi-supervised learning and sampling in networks. The descri...

Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution. We propose a new general controlled, easily distributed algorithm for this task. The algorithm includes as special...

A novel reinforcement learning algorithm is introduced for multiarmed restless bandits with average reward, using the paradigms of Q-learning and Whittle index. Specifically, we leverage the structure of the Whittle index policy to reduce the search space of Q-learning, resulting in major computational gains. Rigorous convergence analysis is provid...

In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria, and we establish that the Cesàro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-...

In this work, we study the spectrum of the normalized Laplacian and its regularized version for random geometric graphs (RGGs) in various scaling regimes. Two scaling regimes are of special interest, the connectivity and the thermodynamic regime. In the connectivity regime, the average vertex degree grows logarithmically in the graph size or faster...

The Whittle index policy is a heuristic that has shown remarkable good performance (with guaranted asymptotic optimality) when applied to the class of problems known as multi-armed restless bandits. In this paper we develop QWI, an algorithm based on Q-learning in order to learn theWhittle indices. The key feature is the deployment of two timescale...

A novel framework called Graph diffusion & PCA (GDPCA) is proposed in the context of semi-supervised learning on graph structured data. It combines a modified Principal Component Analysis with the classical supervised loss and Laplacian regularization, thus handling the case where the adjacency matrix is Sparse and avoiding the Curse of dimensional...

This article studies the recovery of static communities in a temporal network. We introduce a temporal stochastic block model where dynamic interaction patterns between node pairs follow a Markov chain. We render this model versatile by adding degree correction parameters, describing the tendency of each node to start new interactions. We show that...

A search engine maintains local copies of different web pages to provide quick search results. This local cache is kept up-to-date by a web crawler that frequently visits these different pages to track changes in them. Ideally, the local copy should be updated as soon as a page changes on the web. However, finite bandwidth availability and server r...

We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when one orbit is tight but the other orbit goes to infinity in probability. All theoretical results are illustrate...

We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively
$\alpha$
-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. We use this equivalence to sho...

We analyze the DQN reinforcement learning algorithm as a stochastic approximation scheme using the o.d.e. (for ‘ordinary differential equation’) approach and point out certain theoretical issues. We then propose a modified scheme called Full Gradient DQN (FG-DQN, for short) that has a sound theoretical basis and compare it with the original scheme...

We describe a systematic procedure to calculate the resolvent operator for a linear pencil on Banach space and thereby simplify, unify and extend known methods for resolution and representation of marginally stable time series. We pay particular attention to those time series commonly known as unit root processes. The new method uses infinite-lengt...

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It resembles in concept the classical spectral clustering method but uses for partitioning the eigenvector associated...

We analyze the DQN reinforcement learning algorithm as a stochastic approximation scheme using the o.d.e. (for `ordinary differential equation') approach and point out certain theoretical issues. We then propose a modified scheme called Full Gradient DQN (FG-DQN, for short) that has a sound theoretical basis and compare it with the original scheme...

The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealin...

Random geometric graphs have become now a popular object of research. Defined rather simply, these graphs describe real networks much better than classical Erdős–Rényi graphs due to their ability to produce tightly connected communities. The n vertices of a random geometric graph are points in d-dimensional Euclidean space, and two vertices are adj...

In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems with time averaging and time discounting optimality criteria, and we establish that the Ces\'aro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional (ID) linear programming (LP)...

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It resembles in concept the classical spectral clustering method but uses for partitioning the eigenvector associated...

A search engine maintains local copies of different web pages to provide quick search results. This local cache is kept up-to-date by a web crawler that frequently visits these different pages to track changes in them. Ideally, the local copy should be updated as soon as a page changes on the web. However, finite bandwidth availability and server r...

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new L\'evy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learnin...

Graphlet counting is a widely-explored problem in network analysis and has been successfully applied to a variety of applications in many domains, most notatbly bioinformatics, social science and infrastructure network studies.
Efficiently computing graphlet counts remains challenging due to the combinatorial explosion, where a naive enumeration a...

Nowadays, Semi-Supervised Learning (SSL) on citation graph data sets is a rapidly growing area of research. However, the recently proposed graph-based SSL algorithms use a default adjacency matrix with binary weights on edges (citations), that causes a loss of the nodes (papers) similarity information. In this work, therefore, we propose a framewor...

This article studies the estimation of static community memberships from temporally correlated pair interactions represented by an $N$-by-$N$-by-$T$ tensor where $N$ is the number of nodes and $T$ is the length of the time horizon. We present several estimation algorithms, both offline and online, which fully utilise the temporal nature of the obse...

Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution. Without loss of generality, and drawing our motivation from applications to large networks, we interpret this prob...

This paper investigates noisy graph-based semi-supervised learning or community detection. We consider the Stochastic Block Model (SBM), where, in addition to the graph observation, an oracle gives a non-perfect information about some nodes' cluster assignment. We derive the Maximum A Priori (MAP) estimator, and show that a continuous relaxation of...

We argue that graph-constrained dynamic choice with reinforcement can be viewed as a scaled version of a special instance of replicator dynamics. The latter also arises as the limiting differential equation for the empirical measures of a vertex reinforced random walk on a directed graph. We use this equivalence to show that for a class of positive...

The population dynamics for the replicator equation are well studied in continuous time but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly, by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to...

The population dynamics for the replicator equation are well studied in continuous time but
there is less work that explicitly considers the evolution in discrete time. The discrete-time
dynamics can often be justified indirectly, by establishing the relevant evolutionary dynamics for
the corresponding continuous-time system, and then appealing to...

A novel reinforcement learning algorithm is introduced for multiarmed restless bandits with average reward, using the paradigms of Q-learning and Whittle index. Specifically, we leverage the structure of the Whittle index policy to reduce the search space of Q-learning, resulting in major computational gains. Rigorous convergence analysis is provid...

For providing quick and accurate results, a search engine maintains a local snapshot of the entire web. And, to keep this local cache fresh, it employs a crawler for tracking changes across various web pages. However, finite bandwidth availability and server restrictions impose some constraints on the crawling frequency. Consequently, the ideal cra...

For providing quick and accurate results, a search engine maintains a local snapshot of the entire web. And, to keep this local cache fresh, it employs a crawler for tracking changes across various web pages. However, finite bandwidth availability and server restrictions impose some constraints on the crawling frequency. Consequently, the ideal cra...

Network geometries are typically characterized by having a finite spectral dimension (SD), \(d_{s}\) that characterizes the return time distribution of a random walk on a graph. The main purpose of this work is to determine the SD of a variety of random graphs called random geometric graphs (RGGs) in the thermodynamic regime, in which the average v...

We consider a finite state, finite action, zero-sum stochastic games with data defining the game lying in the ordered field of real algebraic numbers. In both the discounted and the limiting average versions of these games, we prove that the value vector also lies in the same field of real algebraic numbers. Our method supplies finite construction...

Random geometric graphs are good examples of random graphs with a tendency to demonstrate community structure. Vertices of such a graph are represented by points in Euclid space , and edge appearance depends on the distance between the points. Random geometric graphs were extensively explored and many of their basic properties are revealed. However...

Network geometries are typically characterized by having a finite spectral dimension (SD), $d_{s}$ that characterizes the return time distribution of a random walk on a graph. The main purpose of this work is to determine the SD of a variety of random graphs called random geometric graphs (RGGs) in the thermodynamic regime, in which the average ver...

In this article, we analyze the limiting eigenvalue distribution (LED) of random geometric graphs (RGGs). The RGG is constructed by uniformly distributing $n$ nodes on the $d$-dimensional torus $\mathbb{T}^d \equiv [0, 1]^d$ and connecting two nodes if their $\ell_{p}$-distance, $p \in [1, \infty]$ is at most $r_{n}$. In particular, we study the LE...

In this work, we study the spectrum of the regularized normalized Laplacian for random geometric graphs (RGGs) in both the connectivity and thermodynamic regimes. We prove that the limiting eigenvalue distribution (LED) of the normalized Laplacian matrix for an RGG converges to the Dirac measure in one in the full range of the connectivity regime....

In a repeated play of a strategic game over infinite horizon, a Nash equilibrium that is played in the long run depends on an initial action profile as well as the way all the players choose their actions at each time.

In semi-supervised graph clustering setting, an expert provides cluster membership of few nodes. This little amount of information allows one to achieve high accuracy clustering using efficient computational procedures. Our main goal is to provide a theoretical justification why the graph-based semi-supervised learning works very well. Specifically...

We study a simple variant of a model pertinent to the asynchronous and distributed calculation of the PageRank centrality on large networks, that has been introduced in the prior computer science community. We show that the system can be reformulate in terms of a model of population dynamics where a random predator is searching for moving preys on...

We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed due to non-uniqueness of solutions, but is amenable to a natural selection principle that picks a unique soluti...

We consider caching of video streams in a cellular network in which each base station is equipped with a cache. Video streams are partitioned into multiple substreams and the goal is to place substreams in caches such that the residual backhaul load is minimized. We consider two coding mechanisms for the substreams: Layered coding (LC) mechanism an...

This book constitutes the refereed proceedings of the 8th EAI International Conference on Game Theory for Networks, GameNets 2019, held in Paris, France, in April 2019.
The 8 full and 3 short papers presented were carefully reviewed and selected from 17 submissions. They are organized in the following topical sections: Game Theory for Wireless Netw...

This book provides a state-of-the-art overview on the dynamics and coevolution in multi-level strategic interaction games. As such it summarizes the results of the European CONGAS project, which developed new mathematical models and tools for the analysis, prediction and control of dynamical processes in systems possessing a rich multi-level struct...

This book constitutes the proceedings of the 16th International Workshop on Algorithms and Models for the Web Graph, WAW 2019, held in Brisbane, QLD, Australia, in July 2019.
The 9 full papers presented in this volume were carefully reviewed and selected from 13 submissions. The papers cover topics of all aspects of algorithmic and mathematical res...

Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart. At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel. The main contribution of the...

We analyse a mean-field model of Personalized PageRank (PPR) on the Erdős–Rényi (ER) random graph containing a denser planted ER subgraph. We investigate the regimes where the values of PPR concentrate around the mean-field value. We also study the optimization of the damping factor, the only parameter in PPR. Our theoretical results help to unders...

The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting
community structure are based on selecting dense subgraphs
inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density
but also the mechanisms of cluster formation...

We consider the consensual distributed optimization problem and propose an asynchronous version of the Alternating Direction Method of Multipliers (ADMM) algorithm to solve it. The `asynchronous' part here refers to the fact that only one node/processor is updated (i.e. performs a minimization step) at each iteration of the algorithm. The selection...

Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two possible 4-node graphlets. The number of each graphlet, called graphlet count, is a signature which characteri...