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In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…
We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…
In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
In recent times, a variety of Reinforcement Learning (RL) algorithms have been proposed for optimal tracking problem of continuous time nonlinear systems with input constraints. Most of these algorithms are based on the notion of uniform…
Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…
This paper presents a spatio-temporal inverse optimal control framework for understanding interactions in multi-agent systems (MAS). We employ a graph representation approach and model the dynamics of interactions between agents as…
In this brief paper, we consider the problem of minimizing the asymptotic exit rate of diffusion processes from an open connected bounded set pertaining to a multi-channel system with small random perturbations. Specifically, we establish a…
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…
This paper deals with solving distributed optimization problems with equality constraints by a class of uncertain nonlinear heterogeneous dynamic multi-agent systems. It is assumed that each agent with an uncertain dynamic model has limited…
The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this…
Sequential decision making for lifetime maximization is a critical problem in many real-world applications, such as medical treatment and portfolio selection. In these applications, a "reneging" phenomenon, where participants may disengage…
This paper studies the decentralized online convex optimization problem for heterogeneous linear multi-agent systems. Agents have access to their time-varying local cost functions related to their own outputs, and there are also…
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…
We propose and compare new global solution algorithms for continuous time heterogeneous agent economies with aggregate shocks. First, we approximate the agent distribution so that equilibrium in the economy can be characterized by a high,…
An autonomous and resilient controller is proposed for leader-follower multi-agent systems under uncertainties and cyber-physical attacks. The leader is assumed non-autonomous with a nonzero control input, which allows changing the team…
Considering that the decision-making environment faced by reinforcement learning (RL) agents is full of Knightian uncertainty, this paper describes the exploratory state dynamics equation in Knightian uncertainty to study the…
A control theoretic approach is presented in this paper for both batch and instantaneous updates of weights in feed-forward neural networks. The popular Hamilton-Jacobi-Bellman (HJB) equation has been used to generate an optimal weight…
Finding Bertram's optimal trading strategy for a pair of cointegrated assets following the Ornstein--Uhlenbeck price difference process can be formulated as an unconstrained convex optimization problem for maximization of expected profit…
In this paper we study a class of HJB equations which solve for equilibria for general time-inconsistent deterministic linear quadratic control problems within the intra-personal game theoretic framework, where the inconsistency arises from…