arXiv subjects

Boualem Djehiche

Publications and source records attributed to Boualem Djehiche.

At least 19 recordsLinked to original sources

arXiv2026

Backpressure-based Mean-field Type Game for Scheduling in Multi-Hop Wireless Sensor Networks

We propose a Mean-Field Type Game (MFTG) framework for effective scheduling in multi-hop wireless sensor networks (WSNs) using backpressure as a performance criterion. Traditional backpressure algorithms leverage queue differentials to regulate data flow and maintain network stability. In this work, we extend the backpressure framework by incorporating a mean-field term into the cost functional, capturing the global behavior of the system alongside local dynamics. The resulting model utilizes the strengths of non-cooperative mean-field type games, enabling nodes to make decentralized decisions based on both individual queue states and system mean-field effects while accounting for stochastic network interactions. By leveraging the interplay between backpressure dynamics and mean-field coupling, the approach balances local optimization with global efficiency. Numerical simulations demonstrate the efficacy of the proposed method in handling congestion and scheduling in large-scale WSNs.

eess.SY↗

arXiv2025

Continuous time Stochastic optimal control under discrete time partial observations

This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for controlling such systems, focusing on the measure-valued process of the system's state and the control actions that depend on noisy and incomplete data. Our approach uses a stochastic optimal control framework with a probability measure-valued state, which accommodates noisy measurements and integrates them into control decisions through a Bayesian update mechanism. We characterize the control optimality in terms of a sequence of interlaced Hamilton Jacobi Bellman (HJB) equations coupled with controlled impulse steps at the measurement times. For the case of Gaussian-controlled processes, we derive an equivalent HJB equation whose state variable is finite-dimensional, namely the state's mean and covariance. We demonstrate the effectiveness of our methods through numerical examples. These include control under perfect observations, control under no observations, and control under noisy observations. Our numerical results highlight significant differences in the control strategies and their performance, emphasizing the challenges and computational demands of dealing with uncertainty in state observation.

math.OC↗

arXiv2025

Breaking the Barriers of Text-Hungry and Audio-Deficient AI

While global linguistic diversity spans more than 7164 recognized languages, the current dominant architecture of machine intelligence remains fundamentally biased toward written text. This bias excludes over 700 million people particularly in rural and remote regions who are audio-literate. In this work, we introduce a fully textless, audio-to-audio machine intelligence framework designed to serve this underserved population, and all the people who prefer audio-efficiency. Our contributions include novel Audio-to-Audio translation architectures that bypass text entirely, including spectrogram-, scalogram-, wavelet-, and unit-based models. Central to our approach is the Multiscale Audio-Semantic Transform (MAST), a representation that encodes tonal, prosodic, speaker, and expressive features. We further integrate MAST into a fractional diffusion of mean-field-type framework powered by fractional Brownian motion. It enables the generation of high-fidelity, semantically consistent speech without reliance on textual supervision. The result is a robust and scalable system capable of learning directly from raw audio, even in languages that are unwritten or rarely digitized. This work represents a fundamental shift toward audio-native machine intelligence systems, expanding access to language technologies for communities historically left out of the current machine intelligence ecosystem.

cs.SD↗

arXiv2025

Convergence rate for random walk approximations of mean field BSDEs

We study the rate of convergence w.r.t.~a Wasserstein type distance for random walk approximations of mean field BSDEs. Our method does not use the particle method but instead a freezing technique. We extend results by Briand, Ch. Geiss, S. Geiss, and Labart [Bernoulli, 27(2) 2021] about the rate of convergence of a Donsker-type theorem for BSDEs from the classical setting to the mean field setting. In this connection the mean field setting leads to new phenomena and requires new techniques that should be of independent interest: The Hölder continuous terminal condition causes a singularity in time of the generator when seen as a generator in the non-mean field setting. To handle this singularity we introduce a concept of modified Hölder continuity by which we are able to achieve, up to a logarithmic term, the same polynomial approximation rates as in the classical non-mean field setting (in fact, already when approximating the Brownian motion itself a logarithmic term is necessary). Moreover, the exploited freezing technique of the mean field terms yields to the problem to handle the quantitative behavior of several different generators. Using BMO-techniques we obtain the rate of convergence for the integrated gradient process in the scale of Lorentz (type) spaces of exponential type.

math.PR↗

arXiv2025

Discrete time stochastic impulse control with delay

We study a class of infinite-horizon impulse control problems with execution delay in discrete time. Using probabilistic methods, particularly the notion of the Snell envelope of processes, we construct an optimal strategy among all admissible strategies for both risk-neutral and risk-sensitive utility functions. Furthermore, we establish the existence of bounded $ε$-optimal strategies. This framework provides a robust approach to handling execution delays in discrete-time stochastic systems.

math.OC↗

arXiv2024

The outcomes of generative AI are exactly the Nash equilibria of a non-potential game

In this article we show that the asymptotic outcomes of both shallow and deep neural networks such as those used in BloombergGPT to generate economic time series are exactly the Nash equilibria of a non-potential game. We then design and analyze deep neural network algorithms that converge to these equilibria. The methodology is extended to federated deep neural networks between clusters of regional servers and on-device clients. Finally, the variational inequalities behind large language models including encoder-decoder related transformers are established.

cs.GT↗

arXiv2023

Time-inconsistent mean-field optimal stopping: A limit approach

We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field diffusion processes and recursive utility functions. Despite the time-inconsistency of the OSP, we show that it is optimal to stop when the value-process hits the reward process for the first time, as is the case for the standard time-consistent OSP. We solve the problem by approximating the corresponding value-process with a sequence of Snell envelopes of processes, for which a sequence of optimal stopping times is constituted of the hitting times of each of the reward processes by the associated value-process. Then, under mild assumptions, we show that this sequence of hitting times converges in probability to the hitting time for the mean-field OSP and that the limit is optimal.

math.PR↗

arXiv2022

Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Type

In this paper, we present an approach to neural network mean-field-type control and its stochastic stability analysis by means of adversarial inputs (aka adversarial attacks). This is a class of data-driven mean-field-type control where the distribution of the variables such as the system states and control inputs are incorporated into the problem. Besides, we present a methodology to validate the feasibility of the approximations of the solutions via neural networks and evaluate their stability. Moreover, we enhance the stability by enlarging the training set with adversarial inputs to obtain a more robust neural network. Finally, a worked-out example based on the linear-quadratic mean-field type control problem (LQ-MTC) is presented to illustrate our methodology.

math.OC↗

arXiv2022

A propagation of chaos result for weakly interacting nonlinear Snell envelopes

In this article, we establish a propagation of chaos result for weakly interacting nonlinear Snell envelopes which converge to a class of mean-field reflected backward stochastic differential equations (BSDEs) with jumps and right-continuous and left-limited obstacle, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters both the driver and the lower obstacle. Under mild Lipschitz and integrability conditions on the coefficients, we prove existence and uniqueness of the solution to both the mean-field reflected BSDEs with jumps and the corresponding system of weakly interacting particles and provide a propagation of chaos result for the whole solution $(Y,Z,U,K)$, which requires new technical results due to the dependence of the obstacle on the solution and the presence of jumps.

math.PR↗

arXiv2022

Zero-sum mean-field Dynkin games: characterization and convergence

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish sufficient conditions under which such a game admits a value and a saddle point. Furthermore, we provide a characterization of the value of the game in terms of a specific class of doubly reflected backward stochastic differential equations (BSDEs) of mean-field type, for which we derive an existence and uniqueness result. We then introduce a corresponding system of weakly interacting zero-sum Dynkin games and show its well-posedness. Finally, we provide a propagation of chaos result for the value of the zero-sum mean-field Dynkin game.

math.OC↗

arXiv2022

Efficient learning of hidden state LTI state space models of unknown order

The aim of this paper is to address two related estimation problems arising in the setup of hidden state linear time invariant (LTI) state space systems when the dimension of the hidden state is unknown. Namely, the estimation of any finite number of the system's Markov parameters and the estimation of a minimal realization for the system, both from the partial observation of a single trajectory. For both problems, we provide statistical guarantees in the form of various estimation error upper bounds, $\rank$ recovery conditions, and sample complexity estimates. Specifically, we first show that the low $\rank$ solution of the Hankel penalized least square estimator satisfies an estimation error in $S_p$-norms for $p \in [1,2]$ that captures the effect of the system order better than the existing operator norm upper bound for the simple least square. We then provide a stability analysis for an estimation procedure based on a variant of the Ho-Kalman algorithm that improves both the dependence on the dimension and the least singular value of the Hankel matrix of the Markov parameters. Finally, we propose an estimation algorithm for the minimal realization that uses both the Hankel penalized least square estimator and the Ho-Kalman based estimation procedure and guarantees with high probability that we recover the correct order of the system and satisfies a new fast rate in the $S_2$-norm with a polynomial reduction in the dependence on the dimension and other parameters of the problem.

math.ST↗

arXiv2021

Importance sampling for a simple Markovian intensity model using subsolutions

This paper considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for e.g. modelling of credit risk. Previous attempts at designing importance sampling algorithms have resulted in poor performance and the main contribution of the paper is the design of efficient importance sampling algorithms using subsolutions. The dynamics of the jump processes causes the corresponding Hamilton-Jacobi equations to have an intricate state-dependence, which makes the design of efficient algorithms difficult. We provide theoretical results that quantify the performance of importance sampling algorithms in general and construct asymptotically optimal algorithms for some examples. The computational gain compared to standard Monte Carlo is illustrated by numerical examples.

math.PR↗

arXiv2021

Non asymptotic estimation lower bounds for LTI state space models with Cramér-Rao and van Trees

We study the estimation problem for linear time-invariant (LTI) state-space models with Gaussian excitation of an unknown covariance. We provide non asymptotic lower bounds for the expected estimation error and the mean square estimation risk of the least square estimator, and the minimax mean square estimation risk. These bounds are sharp with explicit constants when the matrix of the dynamics has no eigenvalues on the unit circle and are rate-optimal when they do. Our results extend and improve existing lower bounds to lower bounds in expectation of the mean square estimation risk and to systems with a general noise covariance. Instrumental to our derivation are new concentration results for rescaled sample covariances and deviation results for the corresponding multiplication processes of the covariates, a differential geometric construction of a prior on the unit operator ball of small Fisher information, and an extension of the Cramér-Rao and van Treesinequalities to matrix-valued estimators.

math.ST↗

arXiv2021

Quantum support vector regression for disability insurance

We propose a hybrid classical-quantum approach for modeling transition probabilities in health and disability insurance. The modeling of logistic disability inception probabilities is formulated as a support vector regression problem. Using a quantum feature map, the data is mapped to quantum states belonging to a quantum feature space, where the associated kernel is determined by the inner product between the quantum states. This quantum kernel can be efficiently estimated on a quantum computer. We conduct experiments on the IBM Yorktown quantum computer, fitting the model to disability inception data from a Swedish insurance company.

stat.CO↗

arXiv2020

Optimal portfolio choice with path dependent benchmarked labor income: a mean field model

We consider the life-cycle optimal portfolio choice problem faced by an agent receiving labor income and allocating her wealth to risky assets and a riskless bond subject to a borrowing constraint. In this paper, to reflect a realistic economic setting, we propose a model where the dynamics of the labor income has two main features. First, labor income adjust slowly to financial market shocks, a feature already considered in Biffis, E., Gozzi, F. and Prosdocimi, C. (2020) - "Optimal portfolio choice with path dependent labor income: the infinite horizon case". Second, the labor income $y_i$ of an agent $i$ is benchmarked against the labor incomes of a population $y^n:=(y_1,y_2,\ldots,y_n)$ of $n$ agents with comparable tasks and/or ranks. This last feature has not been considered yet in the literature and is faced taking the limit when $n\to +\infty$ so that the problem falls into the family of optimal control of infinite dimensional McKean-Vlasov Dynamics, which is a completely new and challenging research field. We study the problem in a simplified case where, adding a suitable new variable, we are able to find explicitly the solution of the associated HJB equation and find the optimal feedback controls.

math.OC↗

arXiv2020

Reflected Backward Stochastic Volterra Integral Equations and related time-inconsistent optimal stopping problems

We study solutions of a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We prove existence and uniqueness by a fixed point argument and we derive a comparison result. Moreover, we show how the solution of our problem is related to a time-inconsistent optimal stopping problem and derive an optimal strategy.

math.PR↗

arXiv2020

Nonlinear reserving and multiple contract modifications in life insurance

Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.

q-fin.MF↗

arXiv2020

Behavior near walls in the mean-field approach to crowd dynamics

This paper introduces a system of stochastic differential equations (SDE) of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at, and move along, walls, by means of sticky boundaries and boundary diffusion. As an alternative to Neumann-type boundary conditions, sticky boundaries and boundary diffusion have a 'smoothing' effect on pedestrian motion. When these effects are active, the pedestrian paths are semimartingales with first-variation part absolutely continuous with respect to the Lebesgue measure $dt$, rather than an increasing processes (which in general induces a measure singular with respect to $dt$) as is the case under Neumann boundary conditions. We show that the proposed mean-field model for pedestrian motion admits a unique weak solution and that it is possible to control the system in the weak sense, using a Pontryagin-type maximum principle. We also relate the mean-field type control problem to the social cost minimization in an interacting particle system. We study the novel model features numerically and we confirm empirical findings on pedestrian crowd motion in congested corridors.

math.OC↗