Tamer Başar

Ashutosh Nayyar, Tamer Basar, Demosthenis Teneketzis et al.

We consider a remote estimation problem with an energy harvesting sensor and a remote estimator. The sensor observes the state of a discrete-time source which may be a finite state Markov chain or a multi-dimensional linear Gaussian system. It harvests energy from its environment (say, for example, through a solar cell) and uses this energy for the purpose of communicating with the estimator. Due to the randomness of energy available for communication, the sensor may not be able to communicate all the time. The sensor may also want to save its energy for future communications. The estimator relies on messages communicated by the sensor to produce real-time estimates of the source state. We consider the problem of finding a communication scheduling strategy for the sensor and an estimation strategy for the estimator that jointly minimize an expected sum of communication and distortion costs over a finite time horizon. Our goal of joint optimization leads to a decentralized decision-making problem. By viewing the problem from the estimator's perspective, we obtain a dynamic programming characterization for the decentralized decision-making problem that involves optimization over functions. Under some symmetry assumptions on the source statistics and the distortion metric, we show that an optimal communication strategy is described by easily computable thresholds and that the optimal estimate is a simple function of the most recently received sensor observation.

Hamidou Tembine, Quanyan Zhu, Tamer Basar

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function described by a Hamilton-Jacobi-Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics.

Ali Khanafer, Tamer Başar, Bahman Gharesifard

We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the disease-free state is the unique equilibrium over the network. Otherwise, an endemic equilibrium state emerges, where some infection remains within the network. Using notions from positive systems theory, {we provide novel proofs for the global asymptotic stability of the equilibrium points in both cases over strongly connected networks based on the value of the basic reproduction number, a fundamental quantity in the study of epidemics.} When the network topology is weakly connected, we provide conditions for the existence, uniqueness, and global asymptotic stability of an endemic state, and we study the stability of the disease-free state. Finally, we demonstrate that the $n$-intertwined Markov model can be viewed as a best-response dynamical system of a concave game among the nodes. This characterization allows us to cast new infection spread dynamics; additionally, we provide a sufficient condition for the global convergence to the disease-free state, which can be checked in a distributed fashion. Several simulations demonstrate our results.

Yanli Liu, Kaiqing Zhang, Tamer Başar et al.

In this paper, we revisit and improve the convergence of policy gradient (PG), natural PG (NPG) methods, and their variance-reduced variants, under general smooth policy parametrizations. More specifically, with the Fisher information matrix of the policy being positive definite: i) we show that a state-of-the-art variance-reduced PG method, which has only been shown to converge to stationary points, converges to the globally optimal value up to some inherent function approximation error due to policy parametrization; ii) we show that NPG enjoys a lower sample complexity; iii) we propose SRVR-NPG, which incorporates variance-reduction into the NPG update. Our improvements follow from an observation that the convergence of (variance-reduced) PG and NPG methods can improve each other: the stationary convergence analysis of PG can be applied to NPG as well, and the global convergence analysis of NPG can help to establish the global convergence of (variance-reduced) PG methods. Our analysis carefully integrates the advantages of these two lines of works. Thanks to this improvement, we have also made variance-reduction for NPG possible, with both global convergence and an efficient finite-sample complexity.

Tamer Basar, Quanyan Zhu

The price of anarchy (PoA) has been widely used in static games to quantify the loss of efficiency due to noncooperation. Here, we extend this concept to a general differential games framework. In addition, we introduce the price of information (PoI) to characterize comparative game performances under different information structures, as well as the price of cooperation to capture the extent of benefit or loss a player accrues as a result of altruistic behavior. We further characterize PoA and PoI for a class of scalar linear quadratic differential games under open-loop and closed-loop feedback information structures. We also obtain some explicit bounds on these indices in a large population regime.

Yongqiang Wang, Tamer Basar

By enabling multiple agents to cooperatively solve a global optimization problem in the absence of a central coordinator, decentralized stochastic optimization is gaining increasing attention in areas as diverse as machine learning, control, and sensor networks. Since the associated data usually contain sensitive information, such as user locations and personal identities, privacy protection has emerged as a crucial need in the implementation of decentralized stochastic optimization. In this paper, we propose a decentralized stochastic optimization algorithm that is able to guarantee provable convergence accuracy even in the presence of aggressive quantization errors that are proportional to the amplitude of quantization inputs. The result applies to both convex and non-convex objective functions, and enables us to exploit aggressive quantization schemes to obfuscate shared information, and hence enables privacy protection without losing provable optimization accuracy. In fact, by using a {stochastic} ternary quantization scheme, which quantizes any value to three numerical levels, we achieve quantization-based rigorous differential privacy in decentralized stochastic optimization, which has not been reported before. In combination with the presented quantization scheme, the proposed algorithm ensures, for the first time, rigorous differential privacy in decentralized stochastic optimization without losing provable convergence accuracy. Simulation results for a distributed estimation problem as well as numerical experiments for decentralized learning on a benchmark machine learning dataset confirm the effectiveness of the proposed approach.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

Learning algorithms are essential for the applications of game theory in a networking environment. In dynamic and decentralized settings where the traffic, topology and channel states may vary over time and the communication between agents is impractical, it is important to formulate and study games of incomplete information and fully distributed learning algorithms which for each agent requires a minimal amount of information regarding the remaining agents. In this paper, we address this major challenge and introduce heterogeneous learning schemes in which each agent adopts a distinct learning pattern in the context of games with incomplete information. We use stochastic approximation techniques to show that the heterogeneous learning schemes can be studied in terms of their deterministic ordinary differential equation (ODE) counterparts. Depending on the learning rates of the players, these ODEs could be different from the standard replicator dynamics, (myopic) best response (BR) dynamics, logit dynamics, and fictitious play dynamics. We apply the results to a class of security games in which the attacker and the defender adopt different learning schemes due to differences in their rationality levels and the information they acquire.

Naci Saldi, Tamer Basar, Maxim Raginsky

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players (agents) and the decentralized nature of this information. When the number of players is sufficiently large and the interactions among agents is of the mean-field type, one way to overcome this challenge is to investigate the infinite-population limit of the problem, which leads to a mean-field game. In this paper, we consider discrete-time partially observed mean-field games with infinite-horizon discounted cost criteria. Using the technique of converting the original partially observed stochastic control problem to a fully observed one on the belief space and the dynamic programming principle, we establish the existence of Nash equilibria for these game models under very mild technical conditions. Then, we show that the mean-field equilibrium policy, when adopted by each agent, forms an approximate Nash equilibrium for games with sufficiently many agents.

Xiaobin Gao, Emrah Akyol, Tamer Basar

This paper considers a sequential sensor scheduling and remote estimation problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process and makes a decision as to whether or not to send this measurement to the estimator. The sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process, over a finite time horizon. The sensor is either charged a cost for each transmission or constrained on transmission times. As opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect (noiseless), in this work an additive noise channel with fixed power constraint is considered; hence, the sensor has to encode its message before transmission. Under some technical assumptions, we obtain the optimal encoding and estimation policies in conjunction with the optimal transmission schedule. The impact of the presence of a noisy channel is analyzed numerically based on dynamic programming. This analysis yields some rather surprising results such as a phase transition phenomenon in the number of used transmission opportunities, which was not encountered in the noiseless communication setting.

Yongqiang Wang, Tamer Basar

Privacy protection and nonconvexity are two challenging problems in decentralized optimization and learning involving sensitive data. Despite some recent advances addressing each of the two problems separately, no results have been reported that have theoretical guarantees on both privacy protection and saddle/maximum avoidance in decentralized nonconvex optimization. We propose a new algorithm for decentralized nonconvex optimization that can enable both rigorous differential privacy and saddle/maximum avoiding performance. The new algorithm allows the incorporation of persistent additive noise to enable rigorous differential privacy for data samples, gradients, and intermediate optimization variables without losing provable convergence, and thus circumventing the dilemma of trading accuracy for privacy in differential privacy design. More interestingly, the algorithm is theoretically proven to be able to efficiently { guarantee accuracy by avoiding} convergence to local maxima and saddle points, which has not been reported before in the literature on decentralized nonconvex optimization. The algorithm is efficient in both communication (it only shares one variable in each iteration) and computation (it is encryption-free), and hence is promising for large-scale nonconvex optimization and learning involving high-dimensional optimization parameters. Numerical experiments for both a decentralized estimation problem and an Independent Component Analysis (ICA) problem confirm the effectiveness of the proposed approach.

Muhammad Aneeq uz Zaman, Alec Koppel, Sujay Bhatt et al.

We consider online reinforcement learning in Mean-Field Games (MFGs). Unlike traditional approaches, we alleviate the need for a mean-field oracle by developing an algorithm that approximates the Mean-Field Equilibrium (MFE) using the single sample path of the generic agent. We call this {\it Sandbox Learning}, as it can be used as a warm-start for any agent learning in a multi-agent non-cooperative setting. We adopt a two time-scale approach in which an online fixed-point recursion for the mean-field operates on a slower time-scale, in tandem with a control policy update on a faster time-scale for the generic agent. Given that the underlying Markov Decision Process (MDP) of the agent is communicating, we provide finite sample convergence guarantees in terms of convergence of the mean-field and control policy to the mean-field equilibrium. The sample complexity of the Sandbox learning algorithm is $\tilde{\mathcal{O}}(ε^{-4})$ where $ε$ is the MFE approximation error. This is similar to works which assume access to oracle. Finally, we empirically demonstrate the effectiveness of the sandbox learning algorithm in diverse scenarios, including those where the MDP does not necessarily have a single communicating class.

Xiangyuan Zhang, Saviz Mowlavi, Mouhacine Benosman et al.

We introduce the receding-horizon policy gradient (RHPG) algorithm, the first PG algorithm with provable global convergence in learning the optimal linear estimator designs, i.e., the Kalman filter (KF). Notably, the RHPG algorithm does not require any prior knowledge of the system for initialization and does not require the target system to be open-loop stable. The key of RHPG is that we integrate vanilla PG (or any other policy search directions) into a dynamic programming outer loop, which iteratively decomposes the infinite-horizon KF problem that is constrained and non-convex in the policy parameter into a sequence of static estimation problems that are unconstrained and strongly-convex, thus enabling global convergence. We further provide fine-grained analyses of the optimization landscape under RHPG and detail the convergence and sample complexity guarantees of the algorithm. This work serves as an initial attempt to develop reinforcement learning algorithms specifically for control applications with performance guarantees by utilizing classic control theory in both algorithmic design and theoretical analyses. Lastly, we validate our theories by deploying the RHPG algorithm to learn the Kalman filter design of a large-scale convection-diffusion model. We open-source the code repository at \url{https://github.com/xiangyuan-zhang/LearningKF}.

Xiangyuan Zhang, Tamer Başar

We revisit in this paper the discrete-time linear quadratic regulator (LQR) problem from the perspective of receding-horizon policy gradient (RHPG), a newly developed model-free learning framework for control applications. We provide a fine-grained sample complexity analysis for RHPG to learn a control policy that is both stabilizing and $ε$-close to the optimal LQR solution, and our algorithm does not require knowing a stabilizing control policy for initialization. Combined with the recent application of RHPG in learning the Kalman filter, we demonstrate the general applicability of RHPG in linear control and estimation with streamlined analyses.

Xiaobin Gao, Emrah Akyol, Tamer Basar

This paper considers a sequential sensor scheduling and remote estimation problem with multiple communication channels. Departing from the classical remote estimation paradigm, which involves one communication channel (noiseless or noisy), we consider here the more realistic setting of two channels with different characteristics (one is cheap but noisy, the other one is costly but noiseless). We first show, via a counter-example, that the common folklore of applying symmetric threshold-based policy, which is well known to be optimal (for unimodal state densities) in the classical remote estimation problem, can no longer be optimal in our setting. In view of that, and in order to make the problem tractable, we introduce a side channel which signals to the receiver the sign of the underlying state. We show, under some technical assumptions, that a threshold-in-threshold based communication scheduling is optimal. The impact of the results is analyzed numerically based on dynamic programming. This numerical analysis reveals some rather surprising results inheriting known properties from the single channel settings, such as not exhausting all the opportunities available for the noisy channel.

Aidin Ferdowsi, Anibal Sanjab, Walid Saad et al.

Competitive resource allocation between adversarial decision makers arises in a wide spectrum of real-world applications such as in communication systems, cyber-physical systems security, as well as financial, political, and electoral competition. As such, developing analytical tools to model and analyze competitive resource allocation is crucial for devising optimal allocation strategies and anticipating the potential outcomes of the competition. To this end, the Colonel Blotto game is one of the most popular game-theoretic frameworks for modeling and analyzing such competitive resource allocation problems. However, in many real-world competitive situations, the Colonel Blotto game does not admit solutions in deterministic strategies and, hence, one must rely on analytically complex mixed-strategies with their associated tractability, applicability, and practicality challenges. In this paper, a generalization of the Colonel Blotto game which enables the derivation of deterministic, practical, and implementable equilibrium strategies is proposed while accounting for the heterogeneity of the battlefields. In addition, the proposed generalized game enables accounting for the consumed resources in each battlefield, a feature that is not considered in the classical Blotto game. For the generalized game, the existence of a Nash equilibrium in pure-strategies is shown. Then, closed-form analytical expressions of the equilibrium strategies, are derived and the outcome of the game is characterized; based on the number of resources of each player as well as the valuation of each battlefield. The generated results provide invaluable insights on the outcome of the competition. For example, the results show that, when both players are fully rational, the more resourceful player can achieve a better total payoff at the Nash equilibrium, a result that is not mimicked in the classical Blotto game.

Ali Khanafer, Behrouz Touri, Tamer Başar

We study the interaction between a network designer and an adversary over a dynamical network. The network consists of nodes performing continuous-time distributed averaging. The goal of the network designer is to assist the nodes reach consensus by changing the weights of a limited number of links in the network. Meanwhile, an adversary strategically disconnects a set of links to prevent the nodes from converging. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. We utilize Pontryagin's Maximum Principle (MP) to tackle both problems and derive the optimal strategies. Although the canonical equations provided by the MP are intractable, we provide an alternative characterization for the optimal strategies that highlights a connection with potential theory. Finally, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for this zero-sum game.

Ali Khanafer, Sourabh Bhattacharya, Tamer Başar

In this work, we study the problem of power allocation and adaptive modulation in teams of decision makers. We consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE).

Xiangyuan Zhang, Weichao Mao, Saviz Mowlavi et al.

We introduce controlgym, a library of thirty-six industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.

Sourabh Bhattacharya, Ali Khanafer, Tamer Başar

In this work, we study the problem of power allocation in teams. Each team consists of two agents who try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams and use {\it{Isaacs'}} approach to obtain the necessary conditions for the optimal trajectories. This leads to a continuous-kernel power allocation game among the players. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy Nash equilibrium (PSNE). Finally, we present simulation results for the case when the agents are holonomic.

Venkata Sriram Siddhardh Nadendla, Emrah Akyol, Cedric Langbort et al.

In this paper, we model a Stackelberg game in a simple Gaussian test channel where a human transmitter (leader) communicates a source message to a human receiver (follower). We model human decision making using prospect theory models proposed for continuous decision spaces. Assuming that the value function is the squared distortion at both the transmitter and the receiver, we analyze the effects of the weight functions at both the transmitter and the receiver on optimal communication strategies, namely encoding at the transmitter and decoding at the receiver, in the Stackelberg sense. We show that the optimal strategies for the behavioral agents in the Stackelberg sense are identical to those designed for unbiased agents. At the same time, we also show that the prospect-theoretic distortions at both the transmitter and the receiver are both larger than the expected distortion, thus making behavioral agents less contended than unbiased agents. Consequently, the presence of cognitive biases increases the need for transmission power in order to achieve a given distortion at both transmitter and receiver.

Ali Khanafer, Tamer Başar

We study the interaction between a network designer and an adversary over a dynamical network. The network consists of nodes performing continuous-time distributed averaging. The adversary strategically disconnects a set of links to prevent the nodes from reaching consensus. Meanwhile, the network designer assists the nodes in reaching consensus by changing the weights of a limited number of links in the network. We formulate two Stackelberg games to describe this competition where the order in which the players act is reversed in the two problems. Although the canonical equations provided by the Pontryagin's maximum principle seem to be intractable, we provide an alternative characterization for the optimal strategies that makes connection to potential theory. Finally, we provide a sufficient condition for the existence of a saddle-point equilibrium for the underlying zero-sum game.

Kaiqing Zhang, Wei Shi, Hao Zhu et al.

In current power distribution systems, one of the most challenging operation tasks is to coordinate the network- wide distributed energy resources (DERs) to maintain the stability of voltage magnitude of the system. This voltage control task has been investigated actively under either distributed optimization-based or local feedback control-based characterizations. The former architecture requires a strongly-connected communication network among all DERs for implementing the optimization algorithms, a scenario not yet realistic in most of the existing distribution systems with under-deployed communication infrastructure. The latter one, on the other hand, has been proven to suffer from loss of network-wide op- erational optimality. In this paper, we propose a game-theoretic characterization for semi-local voltage control with only a locally connected communication network. We analyze the existence and uniqueness of the generalized Nash equilibrium (GNE) for this characterization and develop a fully distributed equilibrium-learning algorithm that relies on only neighbor-to-neighbor information exchange. Provable convergence results are provided along with numerical tests which corroborate the robust convergence property of the proposed algorithm.

Khaled Alshehri, Subhonmesh Bose, Tamer Başar

Wholesale electricity market designs in practice do not provide the market participants with adequate mechanisms to hedge their financial risks. Demanders and suppliers will likely face even greater risks with the deepening penetration of variable renewable resources like wind and solar. This paper explores the design of a centralized cash-settled call option market to mitigate such risks. A cash-settled call option is a financial instrument that allows its holder the right to claim a monetary reward equal to the positive difference between the real-time price of an underlying commodity and a pre-negotiated strike price for an upfront fee. Through an example, we illustrate that a bilateral call option can reduce the payment volatility of market participants. Then, we design a centralized clearing mechanism for call options that generalizes the bilateral trade. We illustrate through an example how the centralized clearing mechanism generalizes the bilateral trade. Finally, the effect of risk preference of the market participants, as well as some generalizations are discussed.

Tamer Basar, Seyed Rasoul Etesami, Alex Olshevsky

We consider the quantized consensus problem on undirected time-varying connected graphs with n nodes, and devise a protocol with fast convergence time to the set of consensus points. Specifically, we show that when the edges of each network in a sequence of connected time-varying networks are activated based on Poisson processes with Metropolis rates, the expected convergence time to the set of consensus points is at most O(n^2 log^2 n), where each node performs a constant number of updates per unit time.

Emrah Akyol, Kenneth Rose, Tamer Basar

This paper considers the problem of optimal zero-delay jamming over an additive noise channel. Early work had already solved this problem for a Gaussian source and channel. Building on a sequence of recent results on conditions for linearity of optimal estimation, and of optimal mappings in source-channel coding, we derive the saddle-point solution to the jamming problem for general sources and channels, without recourse to Gaussian assumptions. We show that linearity conditions play a pivotal role in jamming, in the sense that the optimal jamming strategy is to effectively force both transmitter and receiver to default to linear mappings, i.e., the jammer ensures, whenever possible, that the transmitter and receiver cannot benefit from non-linear strategies. This result is shown to subsume the known result for Gaussian source and channel. We analyze conditions and general settings where such unbeatable strategy can indeed be achieved by the jammer. Moreover, we provide the procedure to approximate optimal jamming in the remaining (source-channel) cases where the jammer cannot impose linearity on the transmitter and the receiver.

Xudong Chen, M. -A. Belabbas, Tamer Basar

We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the average estimation error is minimized. We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specifc equilibrium solution using the concepts of normalized equilibrium and evolutionary stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics such as Brown-von Neumann-Nash dynamics, and replicator dynamics.

Bin Hu, Kaiqing Zhang, Na Li et al.

Gradient-based methods have been widely used for system design and optimization in diverse application domains. Recently, there has been a renewed interest in studying theoretical properties of these methods in the context of control and reinforcement learning. This article surveys some of the recent developments on policy optimization, a gradient-based iterative approach for feedback control synthesis, popularized by successes of reinforcement learning. We take an interdisciplinary perspective in our exposition that connects control theory, reinforcement learning, and large-scale optimization. We review a number of recently-developed theoretical results on the optimization landscape, global convergence, and sample complexity of gradient-based methods for various continuous control problems such as the linear quadratic regulator (LQR), $\mathcal{H}_\infty$ control, risk-sensitive control, linear quadratic Gaussian (LQG) control, and output feedback synthesis. In conjunction with these optimization results, we also discuss how direct policy optimization handles stability and robustness concerns in learning-based control, two main desiderata in control engineering. We conclude the survey by pointing out several challenges and opportunities at the intersection of learning and control.

Muhammed O. Sayin, Tamer Başar

We propose a new defense mechanism against undetected infiltration into controllers in cyber-physical systems. To this end, we cautiously design the outputs of the sensors that monitor the state of the system. Different from the defense mechanisms that seek to detect infiltration, the proposed approach seeks to minimize the damage of possible attacks before they have been detected. Controller of a cyber-physical system could have been infiltrated into by an undetected attacker at any time of the operation. Disregarding such a possibility and disclosing system's state without caution benefits the attacker in his/her malicious objective. Therefore, secure sensor design can improve the security of cyber-physical systems further when incorporated along with other defense mechanisms. We, specifically, consider a controlled Gauss-Markov process, where the controller could have been infiltrated into at any time within the system's operation. In the sense of game-theoretic hierarchical equilibrium, we provide a semi-definite programming based algorithm to compute the optimal linear secure sensor outputs and analyze the performance for various scenarios numerically.

Anibal Sanjab, Walid Saad, Tamer Başar

In this paper, a novel graph-theoretic framework is proposed to generalize the analysis of a broad set of security attacks, including observability and data injection attacks, that target the state estimator of a smart grid. First, the notion of observability attacks is defined based on a proposed graph-theoretic construct. In this respect, a structured approach is proposed to characterize critical sets, whose removal renders the system unobservable. It is then shown that, for the system to be observable, these critical sets must be part of a maximum matching over a proposed bipartite graph. In addition, it is shown that stealthy data injection attacks (SDIAs) constitute a special case of these observability attacks. Then, various attack strategies and defense policies, for observability and data injection attacks, are shown to be amenable to analysis using the introduced graph-theoretic framework. The proposed framework is then shown to provide a unified basis for analysis of four key security problems (among others), pertaining to the characterization of: 1) The sparsest SDIA; 2) the sparsest SDIA including a certain measurement; 3) a set of measurements which must be defended to thwart all potential SDIAs; and 4) the set of measurements, which when protected, can thwart any SDIA whose cardinality is below a certain threshold. A case study using the IEEE 14-bus system with a set of 17 measurements is used to support the theoretical findings.

Xiangyuan Zhang, Bin Hu, Tamer Başar

We develop the first end-to-end sample complexity of model-free policy gradient (PG) methods in discrete-time infinite-horizon Kalman filtering. Specifically, we introduce the receding-horizon policy gradient (RHPG-KF) framework and demonstrate $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity for RHPG-KF in learning a stabilizing filter that is $ε$-close to the optimal Kalman filter. Notably, the proposed RHPG-KF framework does not require the system to be open-loop stable nor assume any prior knowledge of a stabilizing filter. Our results shed light on applying model-free PG methods to control a linear dynamical system where the state measurements could be corrupted by statistical noises and other (possibly adversarial) disturbances.

Quanyan Zhu, Hamidou Tembine, Tamer Basar

In this paper, we formulate an evolutionarymultiple access control game with continuousvariable actions and coupled constraints. We characterize equilibria of the game and show that the pure equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specific equilibrium solution using the concepts of normalized equilibrium and evolutionarily stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics, such as Brown-von Neumann-Nash dynamics, Smith dynamics and replicator dynamics. In addition, we examine correlated equilibrium for the single-receiver model. Correlated strategies are based on signaling structures before making decisions on rates. We then focus on evolutionary games for hybrid additive white Gaussian noise multiple access channel with multiple users and multiple receivers, where each user chooses a rate and splits it over the receivers. Users have coupled constraints determined by the capacity regions. Building upon the static game, we formulate a system of hybrid evolutionary game dynamics using G-function dynamics and Smith dynamics on rate control and channel selection, respectively. We show that the evolving game has an equilibrium and illustrate these dynamics with numerical examples.

Dongsheng Ding, Kaiqing Zhang, Jiali Duan et al.

We study the sequential decision making problem of maximizing the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon optimal control problem for Constrained Markov Decision Processes (constrained MDPs). Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method that updates the primal variable via natural policy gradient ascent and the dual variable via projected subgradient descent. Although the underlying maximization involves a nonconcave objective function and a nonconvex constraint set, under the softmax policy parametrization, we prove that our method achieves global convergence with sublinear rates regarding both the optimality gap and the constraint violation. Such convergence is independent of the size of the state-action space, i.e., it is~dimension-free. Furthermore, for log-linear and general smooth policy parametrizations, we establish sublinear convergence rates up to a function approximation error caused by restricted policy parametrization. We also provide convergence and finite-sample complexity guarantees for two sample-based NPG-PD algorithms. We use a set of computational experiments to showcase the effectiveness of our approach.

Junji Yan, Asrin Efe Yorulmaz, Hanchen Zhou et al.

Modern Graphics Processing Unit (GPU)-backed services must satisfy strict latency service-level objectives (SLOs) while controlling spare-capacity cost. 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 drift in the residual-demand regime. For any fixed price-capacity pair satisfying the drainability guardrail, we establish a unique operating point and global convergence towards it under a checkable step-size condition. Building on this fixed-pair analysis, we further develop an optimizer-agnostic action shield for the full dynamic problem and show empirically that it improves safety and robustness for model-free reinforcement learning (RL) in this setting.

Ashutosh Nayyar, Abhishek Gupta, Cédric Langbort et al.

A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information among the controllers makes it difficult to compute or characterize Nash equilibria. Using common information among the controllers, the game with asymmetric information is shown to be equivalent to another game with symmetric information. Further, under certain conditions, a Markov state is identified for the equivalent symmetric information game and its Markov perfect equilibria are characterized. This characterization provides a backward induction algorithm to find Nash equilibria of the original game with asymmetric information in pure or behavioral strategies. Each step of this algorithm involves finding Bayesian Nash equilibria of a one-stage Bayesian game. The class of Nash equilibria of the original game that can be characterized in this backward manner are named common information based Markov perfect equilibria.

Kang Kang, Sourabh Bhattacharya, Tamer Basar

In this paper, we address the problem of stabilization in continuous time linear dynamical systems using state feedback when compressive sampling techniques are used for state measurement and reconstruction. In [5], we had introduced the concept of using l1 reconstruction technique, commonly used in sparse data reconstruction, for state measurement and estimation in a discrete time linear system. In this work, we extend the previous scenario to analyse continuous time linear systems. We investigate the effect of switching within a set of sparsifiers, introduced in [5], on the stability of a linear plant in continuous time settings. Initially, we analyze the problem of stabilization in low dimensional systems, following which we generalize the results to address the problem of stabilization in systems of arbitrary dimensions.

Dario Bauso, Puduru Viswanadha Reddy, Tamer Basar

This paper considers a dynamic game with transferable utilities (TU), where the characteristic function is a continuous-time bounded mean ergodic process. A central planner interacts continuously over time with the players by choosing the instantaneous allocations subject to budget constraints. Before the game starts, the central planner knows the nature of the process (bounded mean ergodic), the bounded set from which the coalitions' values are sampled, and the long run average coalitions' values. On the other hand, he has no knowledge of the underlying probability function generating the coalitions' values. Our goal is to find allocation rules that use a measure of the extra reward that a coalition has received up to the current time by re-distributing the budget among the players. The objective is two-fold: i) guaranteeing convergence of the average allocations to the core (or a specific point in the core) of the average game, ii) driving the coalitions' excesses to an a priori given cone. The resulting allocation rules are robust as they guarantee the aforementioned convergence properties despite the uncertain and time-varying nature of the coaltions' values. We highlight three main contributions. First, we design an allocation rule based on full observation of the extra reward so that the average allocation approaches a specific point in the core of the average game, while the coalitions' excesses converge to an a priori given direction. Second, we design a new allocation rule based on partial observation on the extra reward so that the average allocation converges to the core of the average game, while the coalitions' excesses converge to an a priori given cone. And third, we establish connections to approachability theory and attainability theory.

Haoran Qiu, Weichao Mao, Archit Patke et al.

Large language models (LLMs) have been driving a new wave of interactive AI applications across numerous domains. However, efficiently serving LLM inference requests is challenging due to their unpredictable execution times originating from the autoregressive nature of generative models. Existing LLM serving systems exploit first-come-first-serve (FCFS) scheduling, suffering from head-of-line blocking issues. To address the non-deterministic nature of LLMs and enable efficient interactive LLM serving, we present a speculative shortest-job-first (SSJF) scheduler that uses a light proxy model to predict LLM output sequence lengths. Our open-source SSJF implementation does not require changes to memory management or batching strategies. Evaluations on real-world datasets and production workload traces show that SSJF reduces average job completion times by 30.5-39.6% and increases throughput by 2.2-3.6x compared to FCFS schedulers, across no batching, dynamic batching, and continuous batching settings.

Shubham Aggarwal, Dipankar Maity, Tamer Başar

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.

Xiangyuan Zhang, Weichao Mao, Haoran Qiu et al.

Closed-loop control of nonlinear dynamical systems with partial-state observability demands expert knowledge of a diverse, less standardized set of theoretical tools. Moreover, it requires a delicate integration of controller and estimator designs to achieve the desired system behavior. To establish a general controller synthesis framework, we explore the Decision Transformer (DT) architecture. Specifically, we first frame the control task as predicting the current optimal action based on past observations, actions, and rewards, eliminating the need for a separate estimator design. Then, we leverage the pre-trained language models, i.e., the Generative Pre-trained Transformer (GPT) series, to initialize DT and subsequently train it for control tasks using low-rank adaptation (LoRA). Our comprehensive experiments across five distinct control tasks, ranging from maneuvering aerospace systems to controlling partial differential equations (PDEs), demonstrate DT's capability to capture the parameter-agnostic structures intrinsic to control tasks. DT exhibits remarkable zero-shot generalization abilities for completely new tasks and rapidly surpasses expert performance levels with a minimal amount of demonstration data. These findings highlight the potential of DT as a foundational controller for general control applications.

Muhammad Aneeq uz Zaman, Alec Koppel, Mathieu Laurière et al.

We address in this paper Reinforcement Learning (RL) among agents that are grouped into teams such that there is cooperation within each team but general-sum (non-zero sum) competition across different teams. To develop an RL method that provably achieves a Nash equilibrium, we focus on a linear-quadratic structure. Moreover, to tackle the non-stationarity induced by multi-agent interactions in the finite population setting, we consider the case where the number of agents within each team is infinite, i.e., the mean-field setting. This results in a General-Sum LQ Mean-Field Type Game (GS-MFTG). We characterize the Nash equilibrium (NE) of the GS-MFTG, under a standard invertibility condition. This MFTG NE is then shown to be $O(1/M)$-NE for the finite population game where $M$ is a lower bound on the number of agents in each team. These structural results motivate an algorithm called Multi-player Receding-horizon Natural Policy Gradient (MRNPG), where each team minimizes its cumulative cost \emph{independently} in a receding-horizon manner. Despite the non-convexity of the problem, we establish that the resulting algorithm converges to a global NE through a novel problem decomposition into sub-problems using backward recursive discrete-time Hamilton-Jacobi-Isaacs (HJI) equations, in which \emph{independent natural policy gradient} is shown to exhibit linear convergence under time-independent diagonal dominance. Numerical studies included corroborate the theoretical results.

Muhammad Aneeq uz Zaman, Shubham Aggarwal, Melih Bastopcu et al.

In this paper, we investigate the impact of introducing relative entropy regularization on the Nash Equilibria (NE) of General-Sum $N$-agent games, revealing the fact that the NE of such games conform to linear Gaussian policies. Moreover, it delineates sufficient conditions, contingent upon the adequacy of entropy regularization, for the uniqueness of the NE within the game. As Policy Optimization serves as a foundational approach for Reinforcement Learning (RL) techniques aimed at finding the NE, in this work we prove the linear convergence of a policy optimization algorithm which (subject to the adequacy of entropy regularization) is capable of provably attaining the NE. Furthermore, in scenarios where the entropy regularization proves insufficient, we present a $δ$-augmentation technique, which facilitates the achievement of an $ε$-NE within the game.

Raj Kiriti Velicheti, Melih Bastopcu, S. Rasoul Etesami et al.

Strategic information disclosure, in its simplest form, considers a game between an information provider (sender) who has access to some private information that an information receiver is interested in. While the receiver takes an action that affects the utilities of both players, the sender can design information (or modify beliefs) of the receiver through signal commitment, hence posing a Stackelberg game. However, obtaining a Stackelberg equilibrium for this game traditionally requires the sender to have access to the receiver's objective. In this work, we consider an online version of information design where a sender interacts with a receiver of an unknown type who is adversarially chosen at each round. Restricting attention to Gaussian prior and quadratic costs for the sender and the receiver, we show that $\mathcal{O}(\sqrt{T})$ regret is achievable with full information feedback, where $T$ is the total number of interactions between the sender and the receiver. Further, we propose a novel parametrization that allows the sender to achieve $\mathcal{O}(\sqrt{T})$ regret for a general convex utility function. We then consider the Bayesian Persuasion problem with an additional cost term in the objective function, which penalizes signaling policies that are more informative and obtain $\mathcal{O}(\log(T))$ regret. Finally, we establish a sublinear regret bound for the partial information feedback setting and provide simulations to support our theoretical results.

Xiangyuan Zhang, Saviz Mowlavi, Mouhacine Benosman et al.

Dimensionality reduction is crucial for controlling nonlinear partial differential equations (PDE) through a "reduce-then-design" strategy, which identifies a reduced-order model and then implements model-based control solutions. However, inaccuracies in the reduced-order modeling can substantially degrade controller performance, especially in PDEs with chaotic behavior. To address this issue, we augment the reduce-then-design procedure with a policy optimization (PO) step. The PO step fine-tunes the model-based controller to compensate for the modeling error from dimensionality reduction. This augmentation shifts the overall strategy into reduce-then-design-then-adapt, where the model-based controller serves as a warm start for PO. Specifically, we study the state-feedback tracking control of PDEs that aims to align the PDE state with a specific constant target subject to a linear-quadratic cost. Through extensive experiments, we show that a few iterations of PO can significantly improve the model-based controller performance. Our approach offers a cost-effective alternative to PDE control using end-to-end reinforcement learning.

Erkan Bayram, Shenyu Liu, Mohamed-Ali Belabbas et al.

Given a training set in the form of a paired $(\mathcal{X},\mathcal{Y})$, we say that the control system $\dot x = f(x,u)$ has learned the paired set via the control $u^*$ if the system steers each point of $\mathcal{X}$ to its corresponding target in $\mathcal{Y}$. If the training set is expanded, most existing methods for finding a new control $u^*$ require starting from scratch, resulting in a quadratic increase in complexity with the number of points. To overcome this limitation, we introduce the concept of $\textit{ tuning without forgetting}$. We develop $\textit{an iterative algorithm}$ to tune the control $u^*$ when the training set expands, whereby points already in the paired set are still matched, and new training samples are learned. At each update of our method, the control $u^*$ is projected onto the kernel of the end-point mapping generated by the controlled dynamics at the learned samples. It ensures keeping the end-points for the previously learned samples constant while iteratively learning additional samples.

Erkan Bayram, Mohamed-Ali Belabbas, Tamer Başar

In this paper, we propose an iterative training algorithm for Neural ODEs that provides models resilient to control (parameter) disturbances. The method builds on our earlier work Tuning without Forgetting-and similarly introduces training points sequentially, and updates the parameters on new data within the space of parameters that do not decrease performance on the previously learned training points-with the key difference that, inspired by the concept of flat minima, we solve a minimax problem for a non-convex non-concave functional over an infinite-dimensional control space. We develop a projected gradient descent algorithm on the space of parameters that admits the structure of an infinite-dimensional Banach subspace. We show through simulations that this formulation enables the model to effectively learn new data points and gain robustness against control disturbance.

Erkan Bayram, Mohamed-Ali Belabbas, Tamer Başar

In our earlier work, we introduced the principle of Tuning without Forgetting (TwF) for sequential training of neural ODEs, where training samples are added iteratively and parameters are updated within the subspace of control functions that preserves the end-point mapping at previously learned samples on the manifold of output labels in the first-order approximation sense. In this letter, we prove that this parameter subspace forms a Banach submanifold of finite codimension under nonsingular controls, and we characterize its tangent space. This reveals that TwF corresponds to a continuation/deformation of the control function along the tangent space of this Banach submanifold, providing a theoretical foundation for its mapping-preserving (not forgetting) during the sequential training exactly, beyond first-order approximation.

Sara Klein, Xiangyuan Zhang, Tamer Başar et al.

In this work, we study $γ$-discounted infinite-horizon tabular Markov decision processes (MDPs) and introduce a framework called dynamic policy gradient (DynPG). The framework directly integrates dynamic programming with (any) policy gradient method, explicitly leveraging the Markovian property of the environment. DynPG dynamically adjusts the problem horizon during training, decomposing the original infinite-horizon MDP into a sequence of contextual bandit problems. By iteratively solving these contextual bandits, DynPG converges to the stationary optimal policy of the infinite-horizon MDP. To demonstrate the power of DynPG, we establish its non-asymptotic global convergence rate under the tabular softmax parametrization, focusing on the dependencies on salient but essential parameters of the MDP. By combining classical arguments from dynamic programming with more recent convergence arguments of policy gradient schemes, we prove that softmax DynPG scales polynomially in the effective horizon $(1-γ)^{-1}$. Our findings contrast recent exponential lower bound examples for vanilla policy gradient.

Asrin Efe Yorulmaz, Raj Kiriti Velicheti, Melih Bastopcu et al.

In this work, we investigate a steering problem in a mediator-augmented two-player normal-form game, where the mediator aims to guide players toward a specific action profile through information and incentive design. We first characterize the games for which successful steering is possible. Moreover, we establish that steering players to any desired action profile is not always achievable with information design alone, nor when accompanied with sublinear payment schemes. Consequently, we derive a lower bound on the constant payments required per round to achieve this goal. To address these limitations incurred with information design, we introduce an augmented approach that involves a one-shot information design phase before the start of the repeated game, transforming the prior interaction into a Stackelberg game. Finally, we theoretically demonstrate that this approach improves the convergence rate of players' action profiles to the target point by a constant factor with high probability, and support it with empirical results.

Weichao Mao, Haoran Qiu, Chen Wang et al.

No-regret learning has a long history of being closely connected to game theory. Recent works have devised uncoupled no-regret learning dynamics that, when adopted by all the players in normal-form games, converge to various equilibrium solutions at a near-optimal rate of $\widetilde{O}(T^{-1})$, a significant improvement over the $O(1/\sqrt{T})$ rate of classic no-regret learners. However, analogous convergence results are scarce in Markov games, a more generic setting that lays the foundation for multi-agent reinforcement learning. In this work, we close this gap by showing that the optimistic-follow-the-regularized-leader (OFTRL) algorithm, together with appropriate value update procedures, can find $\widetilde{O}(T^{-1})$-approximate (coarse) correlated equilibria in full-information general-sum Markov games within $T$ iterations. Numerical results are also included to corroborate our theoretical findings.