Related papers: Covariance steering in zero-sum linear-quadratic t…
In this paper, we present an online learning approach for two-player zero-sum linear quadratic games with unknown dynamics. We develop a framework combining regularized least squares model estimation, high probability confidence sets, and…
This paper studies a two-player nonzero-sum stochastic differential game governed by a controlled convection-diffusion stochastic partial differential equation (SPDE) with spatially heterogeneous coefficients. The diffusion and transport…
In this work, we propose a feedback control based temporal discretization for linear quadratic optimal control problems (LQ problems) governed by controlled mean-field stochastic differential equations. We firstly decompose the original…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
This paper investigates a class of general linear-quadratic mean field games with common noise, where the diffusion terms of the system contain the state variables, control variables, and the average state terms. We solve the problem using…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
We consider a class of stochastic optimal control problems for discrete-time stochastic linear systems which seek for control policies that will steer the probability distribution of the terminal state of the system close to a desired…
In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset $\Gamma$ of full space $\mathbb{R}^m$. The decentralized strategies and consistency…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
We investigate the convergence of symmetric stochastic differential games with interactions via control, where the volatility terms of both idiosyncratic and common noises are controlled. We apply the stochastic maximum principle, following…
We formulate a two-team linear quadratic stochas- tic dynamic game featuring two opposing teams each with decentralized information structures. We introduce the concept of mutual quadratic invariance (MQI), which, analogously to quadratic…
This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters…
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of…
Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…
This paper aims to formulate and study the inverse problem of non-cooperative linear quadratic games: Given a profile of control strategies, find cost parameters for which this profile of control strategies is Nash. We formulate the problem…
We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…
This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium…
In this paper we investigate two-player zero-sum stochastic differential games with an ergodic payoff, in which the diffusion coefficient does not need to be non-degenerate. We first establish the existence of a viscosity solution to the…
In the framework of continuous time symmetric stochastic differential games in open loop strategies, we introduce a generalization of mean field game solution, called coarse correlated solution. This can be seen as the analogue of a coarse…
In this work, we consider the problem of steering the first two moments of the uncertain state of a discrete time nonlinear stochastic system to prescribed goal quantities at a given final time. In principle, the latter problem can be…