Related papers: Inverse Linear-Quadratic Gaussian Differential Gam…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
We address safe multi-robot interaction under uncertainty. In particular, we formulate a chance-constrained linear quadratic Gaussian game with coupling constraints and system uncertainties. We find a tractable reformulation of the game and…
Zero-sum Linear Quadratic (LQ) games are fundamental in optimal control and can be used (i)~as a dynamic game formulation for risk-sensitive or robust control and (ii)~as a benchmark setting for multi-agent reinforcement learning with two…
This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…
This work investigates the ambient potential identification problem in inverse Mean-Field Games (MFGs), where the goal is to recover the unknown potential from the value function at equilibrium. We propose a simple yet effective iterative…
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…
We propose a policy iteration algorithm for solving the multiplicative noise linear quadratic output feedback design problem. The algorithm solves a set of coupled Riccati equations for estimation and control arising from a partially…
Linear Quadratic Gaussian (LQG) systems are well-understood and methods to minimize the expected cost are readily available. Less is known about the statistical properties of the resulting cost function. The contribution of this paper is a…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
Solving hydrologic inverse problems usually requires repetitive forward simulations. One approach to mitigate the computational cost is to build a surrogate model, i.e., an approximate mapping from model parameters (input) to observable…
In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations. Firstly, we establish…
In this paper, we consider a class of linear quadratic extended mean field games (MFGs) with common noises where the state coefficients and the cost functional vary with the mean field term in a nonlinear way. Based on stochastic maximum…
In this paper, we consider the problem of tracking a reference trajectory for a simplified car model based on unicycle kinematics, whose position only is measured, and where the control input and the measurements are corrupted by…
In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these…
We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…
We address the problem of finding conditions which guarantee the existence of open-loop Nash equilibria in discrete time dynamic games (DTDGs). The classical approach to DTDGs involves analyzing the problem using optimal control theory…
This paper investigates the so-called asymptotic solvability problem in linear quadratic (LQ) mean field games. The model has asymptotic solvability if for all sufficiently large population sizes, the corresponding game has a set of…
This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of…
This paper is concerned with a two-person zero-sum indefinite stochastic linear-quadratic Stackelberg differential game with asymmetric informational uncertainties, where both the leader and follower face different and unknown disturbances.…
This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and…