Related papers: Stochastic Target Games and Dynamic Programming vi…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
In this paper we propose a novel semi-definite programming approach that solves reach-avoid problems over open (i.e., not bounded a priori) time horizons for dynamical systems modeled by polynomial stochastic differential equations. The…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost…
Many security and other real-world situations are dynamic in nature and can be modelled as strictly competitive (or zero-sum) dynamic games. In these domains, agents perform actions to affect the environment and receive observations --…
Recent extensions to dynamic games of the well-known fictitious play learning procedure in static games were proved to globally converge to stationary Nash equilibria in two important classes of dynamic games (zero-sum and…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and…
We propose SmoothCruiser, a new planning algorithm for estimating the value function in entropy-regularized Markov decision processes and two-player games, given a generative model of the environment. SmoothCruiser makes use of the…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…
There are only a few learning algorithms applicable to stochastic dynamic teams and games which generalize Markov decision processes to decentralized stochastic control problems involving possibly self-interested decision makers. Learning…
We want to introduce another smoothing approach by treating each geometric element as a player in a game: a quest for the best element quality. In other words, each player has the goal of becoming as regular as possible. The set of…
This paper investigates value function approximation in the context of zero-sum Markov games, which can be viewed as a generalization of the Markov decision process (MDP) framework to the two-agent case. We generalize error bounds from MDPs…
This paper is concerned with stochastic differential games (SDGs) defined through fully coupled forward-backward stochastic differential equations (FBSDEs) which are governed by Brownian motion and Poisson random measure. For SDGs, the…
Dual control explicitly addresses the problem of trading off active exploration and exploitation in the optimal control of partially unknown systems. While the problem can be cast in the framework of stochastic dynamic programming, exact…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
Stochastic two-player games model systems with an environment that is both adversarial and stochastic. In this paper, we study the expected value of bounded quantitative prefix-independent objectives in the context of stochastic games. We…