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In many problems that involve multiple decision making agents, optimal choices for each agent depend on the choices of others. Differential game theory provides a principled formalism for expressing these coupled interactions and recent…
Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear…
We consider the problem of optimally controlling stochastic, Markovian systems subject to joint chance constraints over a finite-time horizon. For such problems, standard Dynamic Programming is inapplicable due to the time correlation of…
This paper considers a class of reinforcement-based learning (namely, perturbed learning automata) and provides a stochastic-stability analysis in repeatedly-played, positive-utility, finite strategic-form games. Prior work in this class of…
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}…
Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…
We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
Conditional Value at Risk (CVaR) is widely used to account for the preferences of a risk-averse agent in the extreme loss scenarios. To study the effectiveness of randomization in interdiction games with an interdictor that is both risk and…
We consider constrained linear-quadratic dynamic games arising in autonomous vehicle platooning, intersection crossing and other cooperative driving scenarios. Infinite-horizon Nash equilibria are reformulated as receding-horizon affine…
This paper addresses a Stackelberg stochastic linear-quadratic (LQ) differential game under closed-loop information, a problem inherently time-inconsistent. Existing approaches rely on solving two coupled Hamilton-Jacobi-Bellman (HJB)…
We consider a class of two-player zero-sum stochastic games with finite state and compact control spaces, which we call stochastic shortest path (SSP) games. They are undiscounted total cost stochastic dynamic games that have a cost-free…
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…
Although dynamic games provide a rich paradigm for modeling agents' interactions, solving these games for real-world applications is often challenging. Many real-world interactive settings involve general nonlinear state and input…
This work introduces a novel control strategy called Iterative Linear Quadratic Regulator for Iterative Tasks (i2LQR), which aims to improve closed-loop performance with local trajectory optimization for iterative tasks in a dynamic…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…
In stochastic games with incomplete information, the uncertainty is evoked by the lack of knowledge about a player's own and the other players' types, i.e. the utility function and the policy space, and also the inherent stochasticity of…
This paper considers a risk-constrained infinite-horizon optimal control problem and proposes to solve it in an iterative manner. Each iteration of the algorithm generates a trajectory from the starting point to the target equilibrium state…
Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal…