Related papers: Covariance steering in zero-sum linear-quadratic t…
Iterative linear-quadratic (ILQ) methods are widely used in the nonlinear optimal control community. Recent work has applied similar methodology in the setting of multiplayer general-sum differential games. Here, ILQ methods are capable of…
We consider the problem of minimum energy steering of a linear stochastic system to a final prescribed distribution over a finite horizon and to maintain a stationary distribution over an infinite horizon. We present sufficient conditions…
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We…
We propose a novel independent and payoff-based learning framework for stochastic games that is model-free, game-agnostic, and gradient-free. The learning dynamics follow a best-response-type actor-critic architecture, where agents update…
In this work, we analyze the properties of the solution to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal cost. In our previous work, we have shown that by utilizing…
In this article, we study a continuous-time stochastic $H_\infty$ control problem based on reinforcement learning (RL) techniques that can be viewed as solving a stochastic linear-quadratic two-person zero-sum differential game (LQZSG).…
This paper considers data-based solutions of linear-quadratic nonzero-sum differential games. Two cases are considered. First, the deterministic game is solved and Nash equilibrium strategies are obtained by using persistently excited data…
This paper studies a stochastic dynamic game between two competing teams, each consisting of a network of collaborating agents. Unlike fully cooperative settings, where all agents share a common objective, each team in this game aims to…
We consider a class of zero-sum stopper vs. singular-controller games in which the controller can only act on a subset $d_0<d$ of the $d$ coordinates of a controlled diffusion. Due to the constraint on the control directions these games…
We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game…
We investigate a two-player zero-sum stochastic differential game problem with the state process being constrained in a connected bounded closed domain, and the cost functional described by the solution of a generalized backward stochastic…
In this paper, we address the inverse problem in the case of linear-quadratic discrete-time dynamic non-cooperative games. Given feedback laws of players that are known to be a Nash equilibrium pair for a discrete-time linear system, we…
This paper is concerned with a linear-quadratic partially observed Stackelberg stochastic differential game with correlated state and observation noises, where the diffusion coefficient does not contain the control variable and the control…
In dynamic noncooperative games, each player makes conjectures about other players' reactions before choosing a strategy. However, resulting equilibria may be multiple and do not always lead to desirable outcomes. These issues are typically…
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…
This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control…
We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by…
We study a two-player nonzero-sum stochastic differential game where one player controls the state variable via additive impulses while the other player can stop the game at any time. The main goal of this work is characterize Nash…
Unlike Poker where the action space $\mathcal{A}$ is discrete, differential games in the physical world often have continuous action spaces not amenable to discrete abstraction, rendering no-regret algorithms with…
A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain…