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Related papers: A Policy Iteration Algorithm for N-player General-…

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We consider a general-sum N-player linear-quadratic game with stochastic dynamics over a finite horizon and prove the global convergence of the natural policy gradient method to the Nash equilibrium. In order to prove the convergence of the…

Optimization and Control · Mathematics 2022-08-16 Ben Hambly , Renyuan Xu , Huining Yang

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

Analysis of PDEs · Mathematics 2021-07-12 Simone Cacace , Fabio Camilli , Alessandro Goffi

We propose projection-free sequential algorithms for linear-quadratic dynamics games. These policy gradient based algorithms are akin to Stackelberg leadership model and can be extended to model-free settings. We show that if the leader…

Systems and Control · Electrical Eng. & Systems 2019-11-13 Jingjing Bu , Lillian J. Ratliff , Mehran Mesbahi

Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm.…

Optimization and Control · Mathematics 2022-03-02 Fabio Camilli , Qing Tang

We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum…

Machine Learning · Computer Science 2019-12-18 Eric Mazumdar , Lillian J. Ratliff , Michael I. Jordan , S. Shankar Sastry

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…

Numerical Analysis · Mathematics 2020-06-29 Diego Zabaljauregui

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…

Optimization and Control · Mathematics 2020-06-29 René Aïd , Francisco Bernal , Mohamed Mnif , Diego Zabaljauregui , Jorge P. Zubelli

We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such…

Optimization and Control · Mathematics 2012-08-03 Marianne Akian , Jean Cochet-Terrasson , Sylvie Detournay , Stéphane Gaubert

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…

Optimization and Control · Mathematics 2025-06-09 Philipp Plank , Yufei Zhang

We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space…

Optimization and Control · Mathematics 2015-03-19 Marianne Akian , Sylvie Detournay

We study policy iteration for infinite-horizon Markov decision processes. It has recently been shown policy iteration style algorithms have exponential lower bounds in a two player game setting. We extend these lower bounds to Markov…

Data Structures and Algorithms · Computer Science 2010-03-18 John Fearnley

Policy gradient methods have become a staple of any single-agent reinforcement learning toolbox, due to their combination of desirable properties: iterate convergence, efficient use of stochastic trajectory feedback, and theoretically-sound…

Computer Science and Game Theory · Computer Science 2025-07-10 Mingyang Liu , Gabriele Farina , Asuman Ozdaglar

We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…

Optimization and Control · Mathematics 2022-02-16 Benjamin Gravell , Iman Shames , Tyler Summers

Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive…

Systems and Control · Electrical Eng. & Systems 2020-03-19 David Fridovich-Keil , Ellis Ratner , Lasse Peters , Anca D. Dragan , Claire J. Tomlin

Autonomous agents should coordinate effectively without prior knowledge of others' intents. While prior work has focused on intent inference, we address the inverse problem: how agents can strategically demonstrate their intents within…

Systems and Control · Electrical Eng. & Systems 2025-11-11 Jingqi Li , Anand Siththaranjan , Somayeh Sojoudi , Claire Tomlin , Andrea Bajcsy

Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…

Optimization and Control · Mathematics 2018-09-25 Bolei Di , Andrew Lamperski

We introduce a contractive abstract dynamic programming framework and related policy iteration algorithms, specifically designed for sequential zero-sum games and minimax problems with a general structure. Aside from greater generality, the…

Computer Science and Game Theory · Computer Science 2021-10-22 Dimitri Bertsekas

We formulate and study a class of two-player zero-sum stochastic dynamic games with partial and asymmetric information. Information asymmetry introduces fundamental challenges involving \emph{belief representation} and \emph{theory of mind}…

Optimization and Control · Mathematics 2026-03-20 Yuxiang Guan , Iman Shames , Tyler Summers

We study the global linear convergence of policy gradient (PG) methods for finite-horizon continuous-time exploratory linear-quadratic control (LQC) problems. The setting includes stochastic LQC problems with indefinite costs and allows…

Optimization and Control · Mathematics 2024-03-05 Michael Giegrich , Christoph Reisinger , Yufei Zhang

This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games (MFG). We reformulate the game as a regenerative problem with deterministic cycles, which allows policy evaluation (PE), policy…

Numerical Analysis · Mathematics 2026-05-18 Shuixin Fang , Shupeng Wang , Zhen Wu , Hui Zhang , Tao Zhou
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