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Konstantin Avrachenkov

Publications and source records attributed to Konstantin Avrachenkov.

At least 19 recordsLinked to original sources
arXiv2026

Extracting and Verifying Illicit Bitcoin Addresses from Underground Forum Discussions

Existing labeled Bitcoin datasets are largely derived from community-reported abuse, blockchain heuristics, incident-specific collections, or proprietary labeling processes. Their construction methods are rarely publicly reproducible and often provide limited evidence that an address was directly involved in illicit activity. We present a reproducible pipeline for constructing evidence-backed Bitcoin labels from HackForums, an underground cybercrime forum with fifteen years of archived activity. The pipeline combines LLM-assisted screening, expert review, and on-chain validation to identify Bitcoin addresses explicitly associated with illicit transactions discussed on the forum. Each released label is supported by contextual evidence from underground discussions and validated on-chain. The resulting dataset contains 2,438 manually verified illicit Bitcoin addresses spanning 2010-2024 and twelve cybercrime categories assigned during LLM screening. We release the dataset, temporal metadata, and the complete extraction pipeline to support reproducible research on cryptocurrency-facilitated cybercrime.

cs.CR↗
arXiv2026

Threshold Structure of Optimal Policies in Restart POMDPs

We study a Restart POMDP (Partially Observable Markov Decision Process) on a general Borel state space, where the controller either lets the hidden state evolve unobserved or restarts the system and observes the new state. Exploiting a sufficient-statistic representation consisting of the last observed state and the elapsed time since restart, we reduce the problem to a fully observed MDP. Under a natural one-step cost deterioration condition, we prove that optimal policies have a threshold structure in the elapsed time for both the discounted and total undiscounted cost criteria. When the state space is partially ordered and the kernel is stochastically monotone, we further show that the optimal threshold is nonincreasing in the state. For the average cost criterion, under additional assumptions of geometric ergodicity and domination of the transient gain, we establish analogous threshold results via the vanishing discount approach, after showing the uniform boundedness of the optimal thresholds and relative value functions.

math.OC↗
arXiv2026

Spectral graph clustering with inhomogeneous latent geometry

We study spectral clustering in the presence of a confounding latent geometry. The leading eigenvectors may then be dominated by the latent geometry rather than by the communities. Nevertheless, we show in a block latent-space model that communities can be recovered from eigenvectors deeper in the spectrum. We analyze the spectral properties of the adjacency matrix through a limiting integral operator and use its structure to develop DBSPEC, a density-based spectral clustering algorithm that requires only approximate localization of the informative eigenvalue and is robust to poor eigenvalue separation. Crucially, this approach handles general latent geometries, overcoming restrictions to homogeneous toroidal models in prior works. Our theoretical predictions for the location of the informative eigenvalue notably align with observations in real-world experiments.

cs.SI↗
arXiv2026

Semi-supervised Community Detection using Glauber Dynamics for an Ising Model

We consider graphs with two communities and analyze an algorithm for learning the community labels when the edges of the graph and only a small fraction of the labels are known in advance. The algorithm is based on the Glauber dynamics for an Ising model where the energy function includes a quadratic penalty on the magnetization. The analysis focuses on graphs sampled from a Stochastic Block Model (SBM) with slowly growing mean degree. We derive a mean-field limit for the magnetization of each community, which can be used to choose the run-time of the algorithm to obtain a target accuracy level. We further prove that almost exact recovery is achieved in a number of iterations that is quasi-linear in the number of nodes. As a special case, our results provide the first rigorous analysis of the label propagation algorithm in the SBM with slowly diverging mean degree. We complement our theoretical results with several numerical experiments.

math.ST↗
arXiv2026

Linking PageRank, Time Reversal, and Policy Evaluation

We establish a connection between policy evaluation in Markov decision processes and PageRank in network analysis. For a fixed policy, we show that the value function of a discounted Markov decision process can be obtained, up to an explicit rescaling, from the PageRank vector of a suitably defined time-reversed Markov chain. In this correspondence, the discount factor plays the role of the teleportation parameter, while rewards induce the restart distribution. Beyond the irreducible case, invoking quasi-stationary distributions and Doob $h$-transforms, we prove a general decomposition theorem showing that policy evaluation for arbitrary finite MDPs reduces to a collection of PageRank problems on the recurrent and transient components of the policy-induced Markov chain. This framework naturally extends to undiscounted MDPs with terminal states and to transition-dependent rewards. We conclude by showing efficiency of our approach on a numerical example of a sticky random walk on large deterministic and random graphs.

math.OC↗
arXiv2026

MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment

Restless Multi-Armed Bandits (RMABs) are powerful models for decision-making under uncertainty, yet classical formulations typically assume fixed dynamics, an assumption often violated in nonstationary environments. We introduce MARBLE (Multi-Armed Restless Bandits in a Latent Markovian Environment), which augments RMABs with a latent Markov state that induces nonstationary behavior. In MARBLE, each arm evolves according to a latent environment state that switches over time, making policy learning substantially more challenging. We further introduce the Markov-Averaged Indexability (MAI) criterion as a relaxed indexability assumption and prove that, despite unobserved regime switches, under the MAI criterion, synchronous Q-learning with Whittle Indices (QWI) converges almost surely to the optimal Q-function and the corresponding Whittle indices. We validate MARBLE on a calibrated simulator-embedded (digital twin) recommender system, where QWI consistently adapts to a shifting latent state and converges to an optimal policy, empirically corroborating our theoretical findings.

cs.LG↗
arXiv2026

Planted clique recovery in random geometric graphs

We investigate the problem of identifying planted cliques in random geometric graphs, focusing on two distinct algorithmic approaches: the first based on vertex degrees (VD) and the other on common neighbors (CN). We analyze the performance of these methods under varying regimes of key parameters, namely the average degree of the graph and the size of the planted clique. We demonstrate that exact recovery is achieved with high probability as the graph size increases, in a specific set of parameters. Notably, our results reveal that the CN-algorithm significantly outperforms the VD-algorithm. In particular, in the connectivity regime, tiny planted cliques (even edges) are correctly identified by the CN-algorithm, yielding a significant impact on anomaly detection. Finally, our results are confirmed by a series of numerical experiments, showing that the devised algorithms are effective in practice.

math.PR↗
arXiv2026

Consistent line clustering using geometric hypergraphs

Subspace clustering becomes inherently difficult near intersections, where points from different subspaces are barely separated. Most existing theoretical results address this issue by imposing separation or sampling assumptions that limit the statistical effect of points near the intersection. We study a minimal setting of two intersecting lines in which the latent sampling law places polynomially large mass in small neighborhoods of the intersection. We derive information-theoretic lower bounds for exact and almost exact recovery under Gaussian noise. In particular, we show that the exact-recovery threshold is determined by the rate at which the latent law concentrates near the intersection. Since any two points are collinear, pairwise information alone does not reveal whether they are sampled from the same latent line. We therefore construct a hypergraph in which nearly collinear triples form hyperedges, and study the resulting hypergraph similarity matrix. Under a simple regularity condition on the latent distribution, we introduce a spectral algorithm that achieves the information-theoretic bounds up to polylogarithmic factors.

math.ST↗
arXiv2026

Community Detection on Block Models with Geometric Kernels

We consider the community recovery problem on a one-dimensional random geometric graph where every node has two independent labels: an observed location label and a hidden community label. A geometric kernel maps the locations of pairs of nodes to probabilities. Edges are drawn between pairs of nodes based on their communities and the value of the kernel corresponding to the respective node locations. Given the graph so generated along with the location labels, the latent communities of the nodes are to be inferred. In this work, we will look into the fundamental statistical limits for recovering the communities in such models. Additionally, we propose a linear-time algorithm (in the number of edges) and show that it recovers the communities of nodes exactly up to the information theoretic threshold.

math.PR↗
arXiv2026

Games with Rational and Herding Players

Classical game theory is a powerful framework to analyze the strategic interactions among rational players. However, in many real-life scenarios, players choose actions based on their inherent natural tendencies rather than deliberate reasoning. In this paper, we develop an analytical framework to study large population games with an alpha-fraction of rational and (1-alpha)-fraction of herding players. We introduce a new notion of equilibrium called alpha-Rational Nash Equilibrium (in short, alpha-RNE) and discuss its interpretations. Some classical equilibria may disappear, and some new ones may emerge, but only for smaller alpha >0. Interestingly, rational players benefit from the presence of herding and may even achieve utility exceeding the socially optimum. Even more strikingly, in some cases, the herding players also benefit, attaining utility close to the social optimum. We further study the effect of the herding fraction on system performance using measures such as the Price of Anarchy (PoA). In transportation networks, a well-known paradox first studied by Pigou and later by Braess typically arises from rational decision-making: adding an extra link can reduce overall efficiency. Our analysis leads to a different conclusion. When a substantial fraction of users exhibit herding behavior, introducing a new link can increase efficiency, provided herding choices can be suitably influenced. The gains are larger when the herding fraction is higher and/or congestion is lower. By contrast, when herding decisions cannot be influenced, the added link may become detrimental. We also study a bandwidth sharing game in which herding tendencies improve system efficiency. Finally, we discuss the mechanism or influence design in the presence of herding, highlighting both opportunities and risks.

math.OC↗
arXiv2026

The Granger-Johansen representation theorem for integrated time series on Banach space

We prove an extended Granger-Johansen representation theorem (GJRT) for finite or infinite order integrated autoregressive time series on Banach space. We assume only that the resolvent of the autoregressive polynomial for the series is analytic on and inside the unit circle except for an isolated singularity at unity. If the singularity is a pole of finite order the time series is integrated of the same order. If the singularity is an essential singularity the time series is integrated of order infinity. When there is no deterministic forcing the value of the series at each time is the sum of an almost surely convergent stochastic trend, a deterministic term depending on the initial conditions and a finite sum of embedded white noise terms in the prior observations. This is the extended GJRT. In each case the original series is the sum of two separate autoregressive time series on complementary subspaces--a singular component which is integrated of the same order as the original series and a regular component which is not integrated. The extended GJRT applies to all integrated autoregressive processes irrespective of the spatial dimension, the number of stochastic trends and cointegrating relations in the system, and the order of integration.

math.FA↗
arXiv2026

Asymptotically Optimal Policies for Weakly Coupled Markov Decision Processes

We consider the problem of maximizing the expected average reward obtained over an infinite time horizon by $n$ weakly coupled Markov decision processes. Our setup is a substantial generalization of the multi-armed restless bandit problem that allows for multiple actions and constraints. We establish a connection with a deterministic and continuous-variable control problem where the objective is to maximize the average reward derived from an occupancy measure that represents the empirical distribution of the processes when $n \to \infty$. We show that a solution of this fluid problem can be used to construct policies for the weakly coupled processes that achieve the maximum expected average reward as $n \to \infty$, and we give sufficient conditions for the existence of solutions. Under certain assumptions on the constraints, we prove that these conditions are automatically satisfied if the unconstrained single-process problem admits a suitable unichain and aperiodic policy. In particular, the assumptions include multi-armed restless bandits and a broad class of problems with multiple actions and inequality constraints. Also, the policies can be constructed in an explicit way in these cases. Our theoretical results are complemented by several concrete examples and numerical experiments, which include multichain setups that are covered by the theoretical results.

math.OC↗
arXiv2025

Lagrangian Index Policy for Restless Bandits with Average Reward

We study the Lagrangian Index Policy (LIP) for restless multi-armed bandits with long-run average reward. In particular, we compare the performance of LIP with the performance of the Whittle Index Policy (WIP), both heuristic policies known to be asymptotically optimal under certain natural conditions. Even though in most cases their performances are very similar, in the cases when WIP shows bad performance, LIP continues to perform very well. We then propose reinforcement learning algorithms, both tabular and NN-based, to obtain online learning schemes for LIP in the model-free setting. The proposed reinforcement learning schemes for LIP require significantly less memory than the analogous schemes for WIP. We calculate analytically the Lagrangian index for the restart model, which applies to the optimal web crawling and the minimization of the weighted age of information. We also give a new proof of asymptotic optimality in case of homogeneous arms as the number of arms goes to infinity, based on exchangeability and de Finetti's theorem.

cs.LG↗
arXiv2025

Constrained Average-Reward Intermittently Observable MDPs

In Markov Decision Processes (MDPs) with intermittent state information, decision-making becomes challenging due to periods of missing observations. Linear programming (LP) methods can play a crucial role in solving MDPs, in particular, with constraints. However, the resultant belief MDPs lead to infinite dimensional LPs, even when the original MDP is with finite state and action spaces. The verification of strong duality becomes non-trivial. This paper investigates the conditions for no duality gap in average-reward finite Markov decision process with intermittent state observations. We first establish that in such MDPs, the belief MDP is unichain if the original Markov chain is recurrent. Furthermore, we establish strong duality of the problem under the same assumption. Finally, we provide a wireless channel example, where the belief state depends on the last channel state received and the age of the channel state. Our numerical results indicate interesting properties of the solution.

math.OC↗
arXiv2025

Stability of Polling Systems for a Large Class of Markovian Switching Policies

We consider a polling system with two queues, where a single server is attending the queues in a cyclic order and requires non-zero switching times to switch between the queues. Our aim is to identify a fairly general and comprehensive class of Markovian switching policies that renders the system stable. Potentially a class of policies that can cover the Pareto frontier related to individual-queue-centric performance measures like the stationary expected number of waiting customers in each queue; for instance, such a class of policies is identified recently for a polling system near the fluid regime (with large arrival and departure rates), and we aim to include that class. We also aim to include a second class that facilitates switching between the queues at the instance the occupancy in the opposite queue crosses a threshold and when that in the visiting queue is below a threshold (this inclusion facilitates design of `robust' polling systems). Towards this, we consider a class of two-phase switching policies, which includes the above mentioned classes. In the maximum generality, our policies can be represented by eight parameters, while two parameters are sufficient to represent the aforementioned classes. We provide simple conditions to identify the sub-class of switching policies that ensure system stability. By numerically tuning the parameters of the proposed class, we illustrate that the proposed class can cover the Pareto frontier for the stationary expected number of customers in the two queues.

math.OC↗
arXiv2025

From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game

Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.

cs.LG↗
arXiv2025

Multi-Community Spectral Clustering for Geometric Graphs

In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clustering algorithm for community recovery on graphs generated by this model. Given such a graph, the algorithm produces an embedding into $\mathbb{R}^{k-1}$ using the eigenvectors associated with the $k-1$ eigenvalues of the adjacency matrix of the graph that are closest to a value determined by the parameters of the model. It then applies $k$-means clustering to the embedding. We prove weak consistency and show that a simple local refinement step ensures strong consistency. A key ingredient is an application of a non-standard version of Davis-Kahan theorem to control eigenspace perturbations when eigenvalues are not simple. We also analyze the limiting spectrum of the adjacency matrix, using a combination of combinatorial and matrix techniques.

cs.SI↗