Tamer Basar

JAAMAS Journal 2026 Journal Article

Computational Markets to Regulate Mobile-Agent Systems

• Jonathan Bredin
• David Kotz
• Tamer Basar

Abstract Mobile-agent systems allow applications to distribute their resource consumption across the network. By prioritizing applications and publishing the cost of actions, it is possible for applications to achieve faster performance than in an environment where resources are evenly shared. We enforce the costs of actions through markets, where user applications bid for computation from host machines. We represent applications as collections of mobile agents and introduce a distributed mechanism for allocating general computational priority to mobile agents. We derive a bidding strategy for an agent that plans expenditures given a budget, and a series of tasks to complete. We also show that a unique Nash equilibrium exists between the agents under our allocation policy. We present simulation results to show that the use of our resource-allocation mechanism and expenditure-planning algorithm results in shorter mean job completion times compared to traditional mobile-agent resource allocation. We also observe that our resource-allocation policy adapts favorably to allocate overloaded resources to higher priority agents, and that agents are able to effectively plan expenditures, even when faced with network delay and job-size estimation error.

JMLR Journal 2025 Journal Article

Convergence and Sample Complexity of Natural Policy Gradient Primal-Dual Methods for Constrained MDPs

• Dongsheng Ding
• Kaiqing Zhang
• Jiali Duan
• Tamer Basar
• Mihailo R. Jovanovic

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. [abs] [ pdf ][ bib ] &copy JMLR 2025. ( edit, beta )

NeurIPS Conference 2025 Conference Paper

Structure Matters: Dynamic Policy Gradient

• Sara Klein
• Xiangyuan Zhang
• Tamer Basar
• Simon Weissmann
• Leif Döring

In this work, we study $\gamma$-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 $(1-\gamma)^{-1}$. Our findings contrast recent exponential lower bound examples for vanilla policy gradient.

JMLR Journal 2023 Journal Article

Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity

• Kaiqing Zhang
• Sham M. Kakade
• Tamer Basar
• Lin F. Yang

Model-based reinforcement learning (RL), which finds an optimal policy after establishing an empirical model, has long been recognized as one of the cornerstones of RL. It is especially suitable for multi-agent RL (MARL), as it naturally decouples the learning and the planning phases, and avoids the non-stationarity problem when all agents are improving their policies simultaneously. Though intuitive and widely-used, the sample complexity of model-based MARL algorithms has not been fully investigated. In this paper, we aim to ad- dress the fundamental question about its sample complexity. We study arguably the most basic MARL setting: two-player discounted zero-sum Markov games, given only access to a generative model. We show that model-based MARL achieves a sample complexity of Oe(|S||A||B|(1 − γ)−3ε−2) for finding the Nash equilibrium (NE) value up to some ε error, and the ε-NE policies with a smooth planning oracle, where γ is the discount factor, and S,A,B denote the state space, and the action spaces for the two agents. We further show that such a sample bound is minimax-optimal (up to logarithmic factors) if the algorithm is reward-agnostic, where the algorithm queries state transition samples without reward knowledge, by establishing a matching lower bound. This is in contrast to the usual reward- aware setting, where the sample complexity lower bound is Ωe(|S|(|A| + |B|)(1 − γ)−3ε−2), and this model-based approach is near-optimal with only a gap on the |A|, |B| dependence. Our results not only illustrate the sample-efficiency of this basic model-based MARL approach, but also elaborate on the fundamental tradeoff between its power (easily handling the reward-agnostic case) and limitation (less adaptive and suboptimal in |A|, |B|), which particularly arises in the multi-agent context. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

NeurIPS Conference 2023 Conference Paper

Multi-Agent Meta-Reinforcement Learning: Sharper Convergence Rates with Task Similarity

• Weichao Mao
• Haoran Qiu
• Chen Wang
• Hubertus Franke
• Zbigniew Kalbarczyk
• Ravishankar Iyer
• Tamer Basar

Multi-agent reinforcement learning (MARL) has primarily focused on solving a single task in isolation, while in practice the environment is often evolving, leaving many related tasks to be solved. In this paper, we investigate the benefits of meta-learning in solving multiple MARL tasks collectively. We establish the first line of theoretical results for meta-learning in a wide range of fundamental MARL settings, including learning Nash equilibria in two-player zero-sum Markov games and Markov potential games, as well as learning coarse correlated equilibria in general-sum Markov games. Under natural notions of task similarity, we show that meta-learning achieves provable sharper convergence to various game-theoretical solution concepts than learning each task separately. As an important intermediate step, we develop multiple MARL algorithms with initialization-dependent convergence guarantees. Such algorithms integrate optimistic policy mirror descents with stage-based value updates, and their refined convergence guarantees (nearly) recover the best known results even when a good initialization is unknown. To our best knowledge, such results are also new and might be of independent interest. We further provide numerical simulations to corroborate our theoretical findings.

NeurIPS Conference 2022 Conference Paper

A Mean-Field Game Approach to Cloud Resource Management with Function Approximation

• Weichao Mao
• Haoran Qiu
• Chen Wang
• Hubertus Franke
• Zbigniew Kalbarczyk
• Ravishankar Iyer
• Tamer Basar

Reinforcement learning (RL) has gained increasing popularity for resource management in cloud services such as serverless computing. As self-interested users compete for shared resources in a cluster, the multi-tenancy nature of serverless platforms necessitates multi-agent reinforcement learning (MARL) solutions, which often suffer from severe scalability issues. In this paper, we propose a mean-field game (MFG) approach to cloud resource management that is scalable to a large number of users and applications and incorporates function approximation to deal with the large state-action spaces in real-world serverless platforms. Specifically, we present an online natural actor-critic algorithm for learning in MFGs compatible with various forms of function approximation. We theoretically establish its finite-time convergence to the regularized Nash equilibrium under linear function approximation and softmax parameterization. We further implement our algorithm using both linear and neural-network function approximations, and evaluate our solution on an open-source serverless platform, OpenWhisk, with real-world workloads from production traces. Experimental results demonstrate that our approach is scalable to a large number of users and significantly outperforms various baselines in terms of function latency and resource utilization efficiency.

ICML Conference 2022 Conference Paper

On Improving Model-Free Algorithms for Decentralized Multi-Agent Reinforcement Learning

• Weichao Mao
• Lin F. Yang
• Kaiqing Zhang
• Tamer Basar

Multi-agent reinforcement learning (MARL) algorithms often suffer from an exponential sample complexity dependence on the number of agents, a phenomenon known as the curse of multiagents. We address this challenge by investigating sample-efficient model-free algorithms in decentralized MARL, and aim to improve existing algorithms along this line. For learning (coarse) correlated equilibria in general-sum Markov games, we propose stage-based V-learning algorithms that significantly simplify the algorithmic design and analysis of recent works, and circumvent a rather complicated no- weighted -regret bandit subroutine. For learning Nash equilibria in Markov potential games, we propose an independent policy gradient algorithm with a decentralized momentum-based variance reduction technique. All our algorithms are decentralized in that each agent can make decisions based on only its local information. Neither communication nor centralized coordination is required during learning, leading to a natural generalization to a large number of agents. Finally, we provide numerical simulations to corroborate our theoretical findings.

NeurIPS Conference 2021 Conference Paper

Decentralized Q-learning in Zero-sum Markov Games

• Muhammed Sayin
• Kaiqing Zhang
• David Leslie
• Tamer Basar
• Asuman Ozdaglar

We study multi-agent reinforcement learning (MARL) in infinite-horizon discounted zero-sum Markov games. We focus on the practical but challenging setting of decentralized MARL, where agents make decisions without coordination by a centralized controller, but only based on their own payoffs and local actions executed. The agents need not observe the opponent's actions or payoffs, possibly being even oblivious to the presence of the opponent, nor be aware of the zero-sum structure of the underlying game, a setting also referred to as radically uncoupled in the literature of learning in games. In this paper, we develop a radically uncoupled Q-learning dynamics that is both rational and convergent: the learning dynamics converges to the best response to the opponent's strategy when the opponent follows an asymptotically stationary strategy; when both agents adopt the learning dynamics, they converge to the Nash equilibrium of the game. The key challenge in this decentralized setting is the non-stationarity of the environment from an agent's perspective, since both her own payoffs and the system evolution depend on the actions of other agents, and each agent adapts her policies simultaneously and independently. To address this issue, we develop a two-timescale learning dynamics where each agent updates her local Q-function and value function estimates concurrently, with the latter happening at a slower timescale.

NeurIPS Conference 2021 Conference Paper

Derivative-Free Policy Optimization for Linear Risk-Sensitive and Robust Control Design: Implicit Regularization and Sample Complexity

• Kaiqing Zhang
• Xiangyuan Zhang
• Bin Hu
• Tamer Basar

Direct policy search serves as one of the workhorses in modern reinforcement learning (RL), and its applications in continuous control tasks have recently attracted increasing attention. In this work, we investigate the convergence theory of policy gradient (PG) methods for learning the linear risk-sensitive and robust controller. In particular, we develop PG methods that can be implemented in a derivative-free fashion by sampling system trajectories, and establish both global convergence and sample complexity results in the solutions of two fundamental settings in risk-sensitive and robust control: the finite-horizon linear exponential quadratic Gaussian, and the finite-horizon linear-quadratic disturbance attenuation problems. As a by-product, our results also provide the first sample complexity for the global convergence of PG methods on solving zero-sum linear-quadratic dynamic games, a nonconvex-nonconcave minimax optimization problem that serves as a baseline setting in multi-agent reinforcement learning (MARL) with continuous spaces. One feature of our algorithms is that during the learning phase, a certain level of robustness/risk-sensitivity of the controller is preserved, which we termed as the implicit regularization property, and is an essential requirement in safety-critical control systems.

ICML Conference 2021 Conference Paper

Near-Optimal Model-Free Reinforcement Learning in Non-Stationary Episodic MDPs

• Weichao Mao
• Kaiqing Zhang
• Ruihao Zhu
• David Simchi-Levi
• Tamer Basar

We consider model-free reinforcement learning (RL) in non-stationary Markov decision processes. Both the reward functions and the state transition functions are allowed to vary arbitrarily over time as long as their cumulative variations do not exceed certain variation budgets. We propose Restarted Q-Learning with Upper Confidence Bounds (RestartQ-UCB), the first model-free algorithm for non-stationary RL, and show that it outperforms existing solutions in terms of dynamic regret. Specifically, RestartQ-UCB with Freedman-type bonus terms achieves a dynamic regret bound of $\widetilde{O}(S^{\frac{1}{3}} A^{\frac{1}{3}} \Delta^{\frac{1}{3}} H T^{\frac{2}{3}})$, where $S$ and $A$ are the numbers of states and actions, respectively, $\Delta>0$ is the variation budget, $H$ is the number of time steps per episode, and $T$ is the total number of time steps. We further show that our algorithm is \emph{nearly optimal} by establishing an information-theoretical lower bound of $\Omega(S^{\frac{1}{3}} A^{\frac{1}{3}} \Delta^{\frac{1}{3}} H^{\frac{2}{3}} T^{\frac{2}{3}})$, the first lower bound in non-stationary RL. Numerical experiments validate the advantages of RestartQ-UCB in terms of both cumulative rewards and computational efficiency. We further demonstrate the power of our results in the context of multi-agent RL, where non-stationarity is a key challenge.

NeurIPS Conference 2020 Conference Paper

An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methods

• Yanli Liu
• Kaiqing Zhang
• Tamer Basar
• Wotao Yin

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 on 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 for the first time, with both global convergence and an efficient finite-sample complexity.

NeurIPS Conference 2020 Conference Paper

Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexity

• Kaiqing Zhang
• Sham Kakade
• Tamer Basar
• Lin Yang

Model-based reinforcement learning (RL), which finds an optimal policy using an empirical model, has long been recognized as one of the cornerstones of RL. It is especially suitable for multi-agent RL (MARL), as it naturally decouples the learning and the planning phases, and avoids the non-stationarity problem when all agents are improving their policies simultaneously using samples. Though intuitive and widely-used, the sample complexity of model-based MARL algorithms has been investigated relatively much less often. In this paper, we aim to address the fundamental open question about the sample complexity of model-based MARL. We study arguably the most basic MARL setting: two-player discounted zero-sum Markov games, given only access to a generative model of state transition. We show that model-based MARL achieves a sample complexity of $\tilde \cO(|\cS||\cA||\cB|(1-\gamma)^{-3}\epsilon^{-2})$ for finding the Nash equilibrium (NE) \emph{value} up to some $\epsilon$ error, and the $\epsilon$-NE \emph{policies}, where $\gamma$ is the discount factor, and $\cS, \cA, \cB$ denote the state space, and the action spaces for the two agents. We also show that this method is near-minimax optimal with a tight dependence on $1-\gamma$ and $|\cS|$ by providing a lower bound of $\Omega(|\cS|(|\cA|+|\cB|)(1-\gamma)^{-3}\epsilon^{-2})$. Our results justify the efficiency of this simple model-based approach in the multi-agent RL setting.

NeurIPS Conference 2020 Conference Paper

Natural Policy Gradient Primal-Dual Method for Constrained Markov Decision Processes

• Dongsheng Ding
• Kaiqing Zhang
• Tamer Basar
• Mihailo Jovanovic

We study sequential decision-making problems in which each agent aims to maximize 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 Constrained Markov Decision Processes (CMDPs) problem. Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method for CMDPs which updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient descent. Even though 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 a convergence is independent of the size of the state-action space, i. e. , it is~dimension-free. Furthermore, for the general smooth policy class, we establish sublinear rates of convergence regarding both the optimality gap and the constraint violation, up to a function approximation error caused by restricted policy parametrization. Finally, we show that two sample-based NPG-PD algorithms inherit such non-asymptotic convergence properties and provide finite-sample complexity guarantees. To the best of our knowledge, our work is the first to establish non-asymptotic convergence guarantees of policy-based primal-dual methods for solving infinite-horizon discounted CMDPs. We also provide computational results to demonstrate merits of our approach.

NeurIPS Conference 2020 Conference Paper

On the Stability and Convergence of Robust Adversarial Reinforcement Learning: A Case Study on Linear Quadratic Systems

• Kaiqing Zhang
• Bin Hu
• Tamer Basar

Reinforcement learning (RL) algorithms can fail to generalize due to the gap between the simulation and the real world. One standard remedy is to use robust adversarial RL (RARL) that accounts for this gap during the policy training, by modeling the gap as an adversary against the training agent. In this work, we reexamine the effectiveness of RARL under a fundamental robust control setting: the linear quadratic (LQ) case. We first observe that the popular RARL scheme that greedily alternates agents’ updates can easily destabilize the system. Motivated by this, we propose several other policy-based RARL algorithms whose convergence behaviors are then studied both empirically and theoretically. We find: i) the conventional RARL framework (Pinto et al. , 2017) can learn a destabilizing policy if the initial policy does not enjoy the robust stability property against the adversary; and ii) with robustly stabilizing initializations, our proposed double-loop RARL algorithm provably converges to the global optimal cost while maintaining robust stability on-the-fly. We also examine the stability and convergence issues of other variants of policy-based RARL algorithms, and then discuss several ways to learn robustly stabilizing initializations. From a robust control perspective, we aim to provide some new and critical angles about RARL, by identifying and addressing the stability issues in this fundamental LQ setting in continuous control. Our results make an initial attempt toward better theoretical understandings of policy-based RARL, the core approach in Pinto et al. , 2017.

NeurIPS Conference 2020 Conference Paper

POLY-HOOT: Monte-Carlo Planning in Continuous Space MDPs with Non-Asymptotic Analysis

• Weichao Mao
• Kaiqing Zhang
• Qiaomin Xie
• Tamer Basar

Monte-Carlo planning, as exemplified by Monte-Carlo Tree Search (MCTS), has demonstrated remarkable performance in applications with finite spaces. In this paper, we consider Monte-Carlo planning in an environment with continuous state-action spaces, a much less understood problem with important applications in control and robotics. We introduce POLY-HOOT, an algorithm that augments MCTS with a continuous armed bandit strategy named Hierarchical Optimistic Optimization (HOO) (Bubeck et al. , 2011). Specifically, we enhance HOO by using an appropriate polynomial, rather than logarithmic, bonus term in the upper confidence bounds. Such a polynomial bonus is motivated by its empirical successes in AlphaGo Zero (Silver et al. , 2017b), as well as its significant role in achieving theoretical guarantees of finite space MCTS (Shah et al. , 2019). We investigate, for the first time, the regret of the enhanced HOO algorithm in non-stationary bandit problems. Using this result as a building block, we establish non-asymptotic convergence guarantees for POLY-HOOT: the value estimate converges to an arbitrarily small neighborhood of the optimal value function at a polynomial rate. We further provide experimental results that corroborate our theoretical findings.

NeurIPS Conference 2020 Conference Paper

Robust Multi-Agent Reinforcement Learning with Model Uncertainty

• Kaiqing Zhang
• Tao Sun
• Yunzhe Tao
• Sahika Genc
• Sunil Mallya
• Tamer Basar

In this work, we study the problem of multi-agent reinforcement learning (MARL) with model uncertainty, which is referred to as robust MARL. This is naturally motivated by some multi-agent applications where each agent may not have perfectly accurate knowledge of the model, e. g. , all the reward functions of other agents. Little a priori work on MARL has accounted for such uncertainties, neither in problem formulation nor in algorithm design. In contrast, we model the problem as a robust Markov game, where the goal of all agents is to find policies such that no agent has the incentive to deviate, i. e. , reach some equilibrium point, which is also robust to the possible uncertainty of the MARL model. We first introduce the solution concept of robust Nash equilibrium in our setting, and develop a Q-learning algorithm to find such equilibrium policies, with convergence guarantees under certain conditions. In order to handle possibly enormous state-action spaces in practice, we then derive the policy gradients for robust MARL, and develop an actor-critic algorithm with function approximation. Our experiments demonstrate that the proposed algorithm outperforms several baseline MARL methods that do not account for the model uncertainty, in several standard but uncertain cooperative and competitive MARL environments.

NeurIPS Conference 2019 Conference Paper

Non-Cooperative Inverse Reinforcement Learning

• Xiangyuan Zhang
• Kaiqing Zhang
• Erik Miehling
• Tamer Basar

Making decisions in the presence of a strategic opponent requires one to take into account the opponent’s ability to actively mask its intended objective. To describe such strategic situations, we introduce the non-cooperative inverse reinforcement learning (N-CIRL) formalism. The N-CIRL formalism consists of two agents with completely misaligned objectives, where only one of the agents knows the true objective function. Formally, we model the N-CIRL formalism as a zero-sum Markov game with one-sided incomplete information. Through interacting with the more informed player, the less informed player attempts to both infer and optimize the true objective function. As a result of the one-sided incomplete information, the multi-stage game can be decomposed into a sequence of single- stage games expressed by a recursive formula. Solving this recursive formula yields the value of the N-CIRL game and the more informed player’s equilibrium strategy. Another recursive formula, constructed by forming an auxiliary game, termed the dual game, yields the less informed player’s strategy. Building upon these two recursive formulas, we develop a computationally tractable algorithm to approximately solve for the equilibrium strategies. Finally, we demonstrate the benefits of our N-CIRL formalism over the existing multi-agent IRL formalism via extensive numerical simulation in a novel cyber security setting.

NeurIPS Conference 2019 Conference Paper

Policy Optimization Provably Converges to Nash Equilibria in Zero-Sum Linear Quadratic Games

• Kaiqing Zhang
• Zhuoran Yang
• Tamer Basar

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconvexity and nonconcavity, zero-sum LQ games have the property that the stationary point of the objective function with respect to the linear feedback control policies constitutes the NE of the game. Building upon this, we develop three projected nested-gradient methods that are guaranteed to converge to the NE of the game. Moreover, we show that all these algorithms enjoy both globally sublinear and locally linear convergence rates. Simulation results are also provided to illustrate the satisfactory convergence properties of the algorithms. To the best of our knowledge, this work appears to be the first one to investigate the optimization landscape of LQ games, and provably show the convergence of policy optimization methods to the NE. Our work serves as an initial step toward understanding the theoretical aspects of policy-based reinforcement learning algorithms for zero-sum Markov games in general.

ICML Conference 2018 Conference Paper

Fully Decentralized Multi-Agent Reinforcement Learning with Networked Agents

• Kaiqing Zhang
• Zhuoran Yang
• Han Liu 0001
• Tong Zhang 0001
• Tamer Basar

We consider the fully decentralized multi-agent reinforcement learning (MARL) problem, where the agents are connected via a time-varying and possibly sparse communication network. Specifically, we assume that the reward functions of the agents might correspond to different tasks, and are only known to the corresponding agent. Moreover, each agent makes individual decisions based on both the information observed locally and the messages received from its neighbors over the network. To maximize the globally averaged return over the network, we propose two fully decentralized actor-critic algorithms, which are applicable to large-scale MARL problems in an online fashion. Convergence guarantees are provided when the value functions are approximated within the class of linear functions. Our work appears to be the first theoretical study of fully decentralized MARL algorithms for networked agents that use function approximation.

AAMAS Conference 2018 Conference Paper

Gossip Gradient Descent

• Yang Liu
• Ji Liu
• Tamer Basar

We consider a problem of learning a linear regression model distributively with a network of N interconnected agents which receive private streaming data. Each agent can deploy an online learning algorithm, e. g. stochastic gradient descent, to learn adaptively the regression model using its receiving private data. The goal is to devise an algorithm for each agent, under the constraint that each of them can communicate only with its neighboring agents based on a communication graph, to enable each agent converge to the true model with a performance comparable to that of the traditional centralized solution. We propose an algorithm called gossip gradient descent, and establish O q log t (1−λ2)N t convergence in expectation and mean square, where λ2 is the second largest eigenvalue of the expected gossip matrix corresponding to the underlying communication graph. For the case when agents are privacy sensitive, we propose a differentially private variant of the algorithm, which achieves ϵ-differential privacy and O r log2 t ϵ(1−λ2)N t! convergence.

IROS Conference 2014 Conference Paper

Numerical approximation for a visibility based pursuit-evasion game

• Sourabh Bhattacharya
• Tamer Basar
• Maurizio Falcone

This work addresses a vision-based target tracking problem between a mobile observer and a target in the presence of a circular obstacle. The task of keeping the target in the observer's field-of-view is modeled as a pursuit-evasion game by assuming that the target is adversarial in nature. Due to the presence of obstacles, this is formulated as a game with state constraints. The objective of the observer is to maintain a line-of-sight with the target at all times. The objective of the target is to break the line-of-sight in finite amount of time. First, we establish that the value of the game exists in this setting. Then we reduce the dimension of the problem by formulating the game in relative coordinates, and present a discretization in time and space for the reduced game. Based on this discretization, we use a fully discrete semi-Lagrangian scheme to compute the Kružkov transform of the value function numerically, and show that the scheme converges for our problem. Finally, we compute the optimal control action of the players from the Kružkov transform of the value function, and demonstrate the performance of the numerical scheme by numerous simulations.

AAMAS Conference 2003 Conference Paper

Coalition Formation in Proportionally Fair Divisible Auctions

• Rajiv T. Maheswaran
• Tamer Basar