Related papers: Mean-field optimal control with stochastic leaders
Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
We develop a limit theory for controlled path-dependent mean field stochastic partial differential equations (SPDEs) within the semigroup approach of Da Prato and Zabczyk. More precisely, we prove existence results for mean field limits and…
In this paper, we investigate a new model of a linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which the leader is allowed to stop her strategy at a random time. Our overarching…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
The leader-following consensus problem of multi-agent systems over finite fields ${\mathbb F}_p$ is considered in this paper. Dynamics of each agent is governed by a linear equation over ${\mathbb F}_p$, where a distributed control protocol…
This paper introduces a system of stochastic differential equations (SDE) of mean-field type that models pedestrian motion. The system lets the pedestrians spend time at, and move along, walls, by means of sticky boundaries and boundary…
This paper investigates a class of unified stochastic linear quadratic Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a {generalized} setting. For each individual agent, the control…
We study stochastic static teams with countably infinite number of decision makers, with the goal of obtaining (globally) optimal policies under a decentralized information structure. We present sufficient conditions to connect the concepts…
In this paper, we study a linear-quadratic partially observed Stackelberg stochastic differential game problem in which a single leader and multiple followers are involved. We consider more practical formulation for partial information that…
Recently, a theory for stochastic optimal control in non-linear dynamical systems in continuous space-time has been developed (Kappen, 2005). We apply this theory to collaborative multi-agent systems. The agents evolve according to a given…
We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle…
Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their…
We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not…
We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…
Opinion dynamics is nowadays a very common field of research. In this article we formulate and then study a novel, namely strategic perspective on such dynamics: There are the usual normal agents that update their opinions, for instance…
This paper is concerned with a linear-quadratic mean field Stackelberg stochastic differential game with partial information and common noise, which contains a leader and a large number of followers. To be specific, the followers face a…
In this paper we consider an optimal control problem for a large population of interacting agents with deterministic dynamics, aggregating potential and constraints on reciprocal distances, in dimension 1. We study existence and qualitative…
We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an…
Existing multi-agent reinforcement learning methods are limited typically to a small number of agents. When the agent number increases largely, the learning becomes intractable due to the curse of the dimensionality and the exponential…