Related papers: Optimal steering to invariant distributions for ne…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -- streets, tracks, etc. -- are inherently undirected and directions are only imposed on them to reduce the danger of…
The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature…
Hierarchies are of fundamental interest in both stochastic optimal control and biological control due to their facilitation of a range of desirable computational traits in a control algorithm and the possibility that they may form a core…
In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the…
We demonstrate that the thermodynamic friction metric governing dissipation in slowly driven continuous-time Markov chains is equivalent to the commute-time embedding and the resistance distance. This equivalence yields complementary…
We present a set-oriented graph-based computational framework for continuous-time optimal transport over nonlinear dynamical systems. We recover provably optimal control laws for steering a given initial distribution in phase space to a…
We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…
The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In…
We consider reversible ergodic Markov chains with finite state space, and we introduce a new notion of quasi-stationary distribution that does not require the presence of any absorbing state. In our setting, the hitting time of the…
This essay provides a comprehensive analysis of the optimization and performance evaluation of various routing algorithms within the context of computer networks. Routing algorithms are critical for determining the most efficient path for…
Using elementary methods, we prove that for a countable Markov chain $P$ of ergodic degree $d > 0$ the rate of convergence towards the stationary distribution is subgeometric of order $n^{-d}$, provided the initial distribution satisfies…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
In this work, we propose distributed and networked energy management scenarios to optimize the production and reservation of energy among a set of distributed energy nodes. In other words, the idea is to optimally allocate the generated and…
A trajectorial large deviation principle is established in a mean field thermodynamic limit for a multiclass loss network with diminishing rates, which may have several stable equilibria. The large deviation limit is identified as a unique…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…