相关论文: Analyzing dynamic decision-making models using Cha…

Partially Observable Markov Decision Processes (POMDP) is a widely used model to represent the interaction of an environment and an agent, under state uncertainty. Since the agent does not observe the environment state, its uncertainty is…

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

In many fields where the main goal is to produce sequential forecasts for decision making problems, the good understanding of the contemporaneous relations among different series is crucial for the estimation of the covariance matrix. In…

We consider a decision maker (DM) who, before taking an action, seeks information by allocating her limited attention dynamically over different news sources that are biased toward alternative actions. Endogenous choice of information…

We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…

We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…

In this paper, we present two methods which generalize static team theory to dynamic team theory, in the context of continuous-time stochastic nonlinear differential decentralized decision systems, with relaxed strategies, which are…

This work introduces a novel deep learning-based architecture, termed the Deep Belief Markov Model (DBMM), which provides efficient, model-formulation agnostic inference in Partially Observable Markov Decision Process (POMDP) problems. The…

We extend opinion dynamics on discourse sheaves to incorporate "directional stubbornness": agents may hold fixed positions in specified directions of their opinion stalk while remaining flexible in others. This converts the equilibrium…

We consider a certain class of nonlinear maps that preserve the probability simplex, i.e., stochastic maps, that are inspired by the DeGroot-Friedkin model of belief/opinion propagation over influence networks. The corresponding dynamical…

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…

Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…

An important question that often arises in the operation of networked systems is whether to collect the real-time data or to estimate them based on the previously collected data. Various factors should be taken into account such as how…

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

Belief dynamics are fundamental to human behavior and social coordination. Individuals rely on accurate beliefs to make decisions, and shared beliefs form the basis of successful cooperation. Traditional studies often examined beliefs in…

In the theory of Partially Observed Markov Decision Processes (POMDPs), existence of optimal policies have in general been established via converting the original partially observed stochastic control problem to a fully observed one on the…

The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…

The dynamics of decisions in complex networks is studied within a Markov process framework using numerical simulations combined with mathematical insight into the process mechanisms. A mathematical discrete-time model is derived based on a…

We consider a sequential decision making process, such as renewable energy trading or electrical production scheduling, whose outcome depends on the future realization of a random factor, such as a meteorological variable. We assume that…