arXiv subjects

Tamer Başar

Publications and source records attributed to Tamer Başar.

At least 19 recordsLinked to original sources

arXiv2026

Conditioning Degenerate Diffusion Models

Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define \emph{approximate} loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.

cs.LG↗

arXiv2026

Privacy Preserving Gossip Learning

We propose a decentralized privacy-preserving learning algorithm in which each agent holds a single private sample and a shared model. Samples are learned sequentially, and each update must preserve the endpoint mappings at previously learned samples while protecting private data. This gives each agent three roles: (i) a learner that updates the model parameters, (ii) a teacher whose sample is learned at the current iteration, and (iii) a protected agent whose sample has already been learned. We build on Tuning without Forgetting (TwF) method to preserve previously learned mappings and show that TwF provides an indistinguishability guarantee for the learner whenever the set of protected agents contains another sample with the same label. For the teacher, we formulate a minimax optimal control problem that models the differential privacy noise as a worst-case disturbance to prevent performance loss while maintaining the same level of privacy for the gradient. For the protected agents, we compute the projections locally and aggregate them using a private push-sum gossip protocol. We prove geometric convergence of the decentralized gossip algorithm and of the distributed projection for TwF.

cs.LG↗

arXiv2026

Adaptive Agent Design

We consider an agent acting against a general non-Markovian environment. The agent maintains its agent states, but is free to choose a transition kernel across those states and optimize its state-feedback control policies. We study the bi-level agent design problem that optimizes the transition kernel and the policy it induces, given said kernel with offline data of observations and actions obtained via a behavioral policy. For general environments, we show that a soft $Q$-learning algorithm converges almost surely to the fixed point of a soft Bellman equation defined by the stationary averages that the behavioral policy and the chosen kernel induce, and we delineate what separates the resulting policy from an optimal one. In partially observed Markov decision problems, we analyze convergence properties of parametrized transition kernel design via zero-th order and Bayesian optimization techniques.

eess.SY↗

arXiv2026

Infinite Horizon Mean-Field Terminal Value Problem

We introduce a class of finite- and infinite-horizon discrete-time control problems for studying macroscale systems in discrete time, which we refer to as mean-field terminal value problems (MFTVPs). An MFTVP takes a terminal $Q$-function as input and, starting from this terminal $Q$-function, seeks an indefinite backward evolution of optimal policies and state measures, as required for an infinite-horizon non-stationary mean-field equilibrium (MFE) of a discrete-time mean-field game (MFG). We study the existence and uniqueness properties of this problem. As an application, using the uniqueness properties of MFTVPs, we show that, in the average-cost setting (and in the discounted setting for sufficiently small discount factors), MFTVPs can be used as an intermediate step to develop approximation schemes between finite-horizon MFEs and average-cost MFEs (respectively, stationary MFEs). In contrast to approaches that use infinite-horizon MFGs as intermediate problems, MFTVPs can be employed when the discount factor is sufficiently small (or, in the average-cost setting, when the drift factor is sufficiently small), together with a regularizer, to approximate a stationary MFE. Assuming uniqueness of the solution of a MFTVP, the restrictions we impose on the Lipschitz parameters of the system are weaker than the contraction conditions available for regularized stationary MFGs, and our approximation scheme remains applicable even in the presence of multiple stationary MFEs.

math.OC↗

arXiv2026

Variational Contraction Conditions for Iterative Algorithms in Multi-Population Discrete-Time Regularized Mean-Field Games

In this work, we study the contraction conditions of iterative algorithms for stationary and finite-horizon discrete-time regularized mean-field games (MFGs) with multiple populations, where each population only interacts with the state distributions of the other populations. Due to the high dimensionality caused by the interaction of different populations, contraction rates for these algorithms cannot, in general, be expressed in terms of radicals. By studying the dynamics of these iterative algorithms and assuming that the system components of each population's MFG are Lipschitz continuous, we present explicit (eventual) contraction conditions for each algorithm in any normed space, relying only on these Lipschitz parameters. As a consequence of these contraction conditions, we provide convergence rates of finite-horizon mean-field equilibria to infinite-horizon stationary (and non-stationary) mean-field equilibria (MFEs), under restrictions on a variational characterization of the dynamics of these iterative algorithms. In the single-population case, the restrictions we impose on this variational characterization to obtain these convergence results are less restrictive than previous results in the literature.

math.OC↗

arXiv2026

Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games

We study contraction properties of non-stationary continuous-time mean-field games (MFGs) under discounting and entropy regularization. The state of the representative agent evolves according to a controlled continuous-time Markov chain, and both the state and action spaces are finite. In contrast to the undiscounted case, we show that, under a sufficiently large discount rate, finite-horizon MFGs admit a horizon-independent contraction condition, which also coincides with the corresponding infinite-horizon non-stationary contraction condition. As a byproduct, we obtain an explicit convergence rate between finite- and infinite-horizon mean-field equilibria. For each finite horizon, we further derive a refined contraction criterion from the spectral radius of a positive operator that majorizes the propagation of policy errors, and show that its large-horizon limit agrees with the horizon-independent contraction factor. Finally, we provide an explicit error bound between discounted and undiscounted finite-horizon regularized equilibria.

cs.GT↗

arXiv2026

A Stackelberg Game Framework with Drainability Guardrails for Pricing and Scaling in Multi-Tenant GPU Cloud Platforms

Modern Graphics Processing Unit (GPU)-backed services must satisfy strict latency service-level objectives (SLOs) while controlling spare-capacity costs. In multi-tenant GPU cloud platforms, this trade-off is inherently dynamic because workload demand is endogenous; specifically, pricing shapes the submissions of heterogeneous tenants, which subsequently impact congestion and delay. We formulate the joint pricing-and-scaling problem as a large-population Stackelberg game problem, and we derive an explicit equilibrium demand map. The resulting closed-loop model reveals a structural failure mode in which delay-insensitive workloads sustain a residual demand floor, making the backlog undrainable under bounded price and service capacity. This observation motivates a computable drainability guardrail that certifies uniformly negative backlog drift in the residual-demand regime. For any fixed price-capacity pair satisfying the drainability guardrail, we establish global convergence to a unique operating point under a checkable step-size condition. Building on this fixed-pair analysis, we further develop an optimizer-agnostic action shield that provides a negative-drift certificate for shielded execution in the residual regime of the dynamic problem and show empirically that it improves safety and robustness for model-free reinforcement learning (RL) in this setting.

cs.GT↗

arXiv2026

Monotone Inclusion Approach to Weakly Monotone Discrete-Time Finite-Horizon Mean-Field Games

We revisit the problem of computing mean-field equilibria (MFEs) in discrete-time, monotone, finite-horizon mean-field games (MFGs). We show that, when the transition kernel is independent of the state-measure term and the reward function satisfies the usual weak monotonicity condition and is Lipschitz continuous, anchored proximal gradient descent methods can be used to compute a monotone MFE. We also establish last-iterate convergence results for these methods. Our approach relies on formulating the computation problem as an optimization problem over the space of occupation measures. Using this formulation, we show that the problem is equivalent to a class of constrained Lipschitz monotone inclusion problems. We then apply iterative methods for this monotone inclusion formulation to derive a tractable algorithm. The resulting algorithm achieves a convergence rate of $O(1/\sqrt{T})$ after $T$ iterations, without requiring any regularization. This rate holds even in the absence of a uniqueness assumption for the corresponding MFE.

math.OC↗

arXiv2026

Shared Infrastructure Investment and Pricing: Stackelberg Equilibria in Risk-Aware Take-or-Pay Contracts

We study a shared infrastructure deployed by an Infrastructure Provider (InP) and used by multiple firms generating revenues through resource usage. We focus on a challenging setting where (i) infrastructure deployment requires substantial upfront investment, which the InP recovers via payments by firms that depend on their uncertain future revenues; (ii) firms' resource usage is jointly influenced by exogenous factors, infrastructure pricing, operational costs, and resource congestion; and (iii) firms exhibit heterogeneous risk aversion. These aspects are typical of emerging technologies, such as Mobile Edge Computing (MEC). Yet, their joint effect on the InP's capacity dimensioning and pricing decisions and the firms' usage commitments remains poorly understood. We establish conditions for the uniqueness of the equilibrium among the firms. We do so by introducing a Stackelberg game with risk-aware take-or-pay contracting and firm-side operational and congestion costs, in which the InP acts as the leader, while firms act as followers that share the infrastructure and commit upfront to future resource usage under uncertain revenues. Followers' heterogeneous risk aversion is modeled through Conditional Value-at-Risk (CVaR). We prove the existence of a Stackelberg equilibrium (SE), in which the followers' decisions constitute a generalized Nash equilibrium, and develop a polynomial-time algorithm that boundedly approximates the SE. We derive a lower bound on the followers' Probability of Profit (PoP). Simulations in a realistic MEC scenario show that higher followers' risk aversion reduces capacity, pricing, and leader profit, while increasing the lower bound on PoP.

cs.GT↗

arXiv2026

Vector-Valued Gossip over $w$-Holonomic Networks

We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a sequence of pairs of adjacent agents communicating and updating their states based on the edge matrix weight. Our key contribution is providing conditions for the convergence of this non-homogeneous Markov process as well as the characterization of its limit set. To this end, we introduce the notion of "$w$-holonomy" of a set of stochastic matrices, which enables the characterization of sequences of gossiping pairs resulting in reaching a desired consensus in a decentralized manner. Stated otherwise, our result characterizes the limiting behavior of infinite products of (non-commuting, possibly with absorbing states) stochastic matrices.

math.OC↗

arXiv2026

Network-Induced Strategic Communication in Opinion Dynamics

Classical opinion dynamics typically assume a fixed mapping from private opinions to public signals, such as linear exchange, saturated signaling, or discrete public actions. In this paper, we show that these communication mappings can be derived from a strategic communication game played on a weighted influence network. Each agent acts as a receiver estimating its neighbors' states and as a sender broadcasting a public signal to influence its audience. We prove that the network's effect on a sender is summarized by a scalar, network-induced exaggeration factor, and the network game decouples into independent scalar cheap talk problems. The communication rules then emerge as behavioral regimes of one model: aligned incentives recover linear averaging; persuasive senders facing naive receivers produce saturated signaling; and persuasive senders facing Bayesian receivers cannot credibly reveal their opinions, so equilibrium communication becomes an interval quantizer, providing a game-theoretic foundation for continuous-opinion discrete-action (CODA) dynamics. Embedded in repeated opinion updates, the resulting strategic-CODA dynamics preserve opinion clustering and exclude extremism. The model predicts that a speaker exaggerates more when their audience is less influenced by them, and that under strong exaggeration, credible public expression collapses to a binary stance even while private opinions remain continuous.

eess.SY↗

arXiv2026

Continuity of VaR and Continuous Differentiability of CVaR under Decision-Dependent Losses

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are widely used in risk-aware optimization and equilibrium models. When the loss depends on a decision variable, the induced distribution, the VaR threshold, and the CVaR tail set all change with the decision. This makes the regularity of the VaR and CVaR maps nontrivial. We give simple sufficient conditions under which the VaR map is continuous and the corresponding CVaR map is continuously differentiable. The assumptions are local around the VaR level and rely on dominated pathwise differentiability of the scenario-wise loss. We also derive the CVaR gradient formula, thereby justifying first-order analysis for decision-dependent tail-risk models.

cs.GT↗

arXiv2026

Cooperative and Noncooperative Paradigms for Game-Theoretic Control of Socio-Technical Systems

This tutorial presents cooperative and noncooperative game-theoretic frameworks for modeling, learning, and control in socio-technical systems, where human behavior, incentives, institutions, and social interactions are coupled with cyber-physical and networked infrastructures. The paper reviews strategic, dynamic, cooperative, matching, learning, and feedback-control approaches for analyzing how local decision-making, adaptation, and strategic interactions shape collective system outcomes. The tutorial further develops feedback-learning and incentive-design perspectives that connect equilibrium analysis with adaptation, distributed control, and mechanism design under information and coordination constraints. We also examine resilience and security challenges arising from adversarial behavior, misinformation, disruptions, and cascading failures in interconnected socio-technical networks. Finally, we discuss emerging research directions at the intersection of game theory, control, learning, and network science for resilient and adaptive socio-technical systems.

eess.SY↗

arXiv2026

Approximation of Discrete-Time Infinite-Horizon Mean-Field Equilibria via Finite-Horizon Mean-Field Equilibria

We address in this paper a fundamental question that arises in mean-field games (MFGs), namely whether mean-field equilibria (MFE) for discrete-time finite-horizon MFGs can be used to obtain approximate stationary as well as non-stationary MFE for similarly structured infinite-horizon MFGs. We provide a rigorous analysis of this relationship, and show that any accumulation point of MFE of a discounted finite-horizon MFG constitutes, under weak convergence as the time horizon goes to infinity, a non-stationary MFE for the corresponding infinite-horizon MFG. Further, under certain conditions, these non-stationary MFE converge to a stationary MFE, establishing the appealing result that finite-horizon MFE can serve as approximations for stationary MFE. Additionally, we establish improved contraction rates for iterative methods used to compute regularized MFE in finite-horizon settings, extending existing results in the literature. As a byproduct, we obtain that when two MFGs have finite-horizon MFE that are close to each other, the corresponding stationary MFE are also close. As one application of the theoretical results, we show that finite-horizon MFGs can facilitate learning-based approaches to approximate infinite-horizon MFE when system components are unknown. Under further assumptions on the Lipschitz coefficients of the regularized system components (which are stronger than contractivity of finite-horizon MFGs), we obtain exponentially decaying finite-time error bounds -- in the time horizon -- between finite-horizon non-stationary, infinite-horizon non-stationary, and stationary MFE. As a byproduct of our error bounds, we present a new uniqueness criterion for infinite-horizon nonstationary MFE beyond the available contraction results in the literature.

math.OC↗

arXiv2026

Nested Extremum Seeking Converges to Stackelberg Equilibrium

The nested Extremum Seeking (nES) algorithm is a model-free optimization method that has been shown to converge to a neighborhood of a Nash equilibrium. In this work, we demonstrate that the same nES dynamics can instead be made to converge to a neighborhood of a Stackelberg (leader--follower) equilibrium by imposing a different scaling law on the algorithm's design parameters. For the two--level nested case, using Lie--bracket averaging and singular perturbation arguments, we provide a rigorous stability proof showing semi-global practical asymptotic convergence to a Stackelberg equilibrium under appropriate time-scale separation. The results reveal that equilibrium selection, Nash versus Stackelberg, depends not on modifying the closed-loop dynamics, but on the hierarchical scaling of design parameters and the induced time-scale structure. We demonstrate this effect using a simple quadratic example and the canonical Fish War game. The Stackelberg variant of nES provides a model-free framework for hierarchical optimization in multi-time-scale systems, with potential applications in power grids, networked dynamical systems, and tuning of particle accelerators.

math.OC↗

arXiv2026

Meta-Learning for Repeated Bayesian Persuasion

Classical Bayesian persuasion studies how a sender influences receivers through carefully designed signaling policies within a single strategic interaction. In many real-world environments, such interactions are repeated across multiple games, creating opportunities to exploit structural similarity across tasks. In this work, we introduce Meta-Persuasion algorithms, establishing the first line of theoretical results for both full-feedback and bandit-feedback settings in the Online Bayesian Persuasion (OBP) and Markov Persuasion Process (MPP) frameworks. We show that our proposed meta-persuasion algorithms achieve provably sharper regret rates under natural notions of task similarity, improving upon the best-known convergence rates for both OBP and MPP. At the same time, they recover the standard single-game guarantees when the sequence of games is picked arbitrarily. Finally, we complement our theoretical analysis with numerical experiments that highlight our regret improvements and the benefits of meta-learning in repeated persuasion environments.

cs.GT↗

arXiv2025

The Silence that Speaks: Neural Estimation via Communication Gaps

Accurate remote state estimation is a fundamental component of many autonomous and networked dynamical systems, where multiple decision-making agents interact and communicate over shared, bandwidth-constrained channels. These communication constraints introduce an additional layer of complexity, namely, the decision of when to communicate. This results in a fundamental trade-off between estimation accuracy and communication resource usage. Traditional extensions of classical estimation algorithms (e.g., the Kalman filter) treat the absence of communication as 'missing' information. However, silence itself can carry implicit information about the system's state, which, if properly interpreted, can enhance the estimation quality even in the absence of explicit communication. Leveraging this implicit structure, however, poses significant analytical challenges, even in relatively simple systems. In this paper, we propose CALM (Communication-Aware Learning and Monitoring), a novel learning-based framework that jointly addresses the dual challenges of communication scheduling and estimator design. Our approach entails learning not only when to communicate but also how to infer useful information from periods of communication silence. We perform comparative case studies on multiple benchmarks to demonstrate that CALM is able to decode the implicit coordination between the estimator and the scheduler to extract information from the instances of 'silence' and enhance the estimation accuracy.

eess.SY↗

arXiv2025

Beyond Gaussian Assumptions: A General Fractional HJB Control Framework for Lévy-Driven Heavy-Tailed Channels in 6G

Emerging 6G wireless systems suffer severe performance degradation in challenging environments like high-speed trains traversing dense urban corridors and Unmanned Aerial Vehicles (UAVs) links over mountainous terrain. These scenarios exhibit non-Gaussian, non-stationary channels with heavy-tailed fading and abrupt signal fluctuations. To address these challenges, this paper proposes a novel wireless channel model based on symmetric $α$-stable Lévy processes, thereby enabling continuous-time state-space characterization of both long-term and short-term fading. Building on this model, a generalized optimal control framework is developed via a fractional Hamilton-Jacobi-Bellman (HJB) equation that incorporates the Riesz fractional operator to capture non-local spatial effects and memory-dependent dynamics. The existence and uniqueness of viscosity solutions to the fractional HJB equation are rigorously established, thus ensuring the theoretical validity of the proposed control formulation. Numerical simulations conducted in a multi-cell, multi-user downlink setting demonstrate the effectiveness of the fractional HJB-based strategy in optimizing transmission power under heavy-tailed co-channel and multi-user interference.

eess.SY↗