18 research outputs found
Bayesian learning without recall
We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the actions of their neighboring agents at each time. Successive applications of Bayes rule to the entire history of past observations lead to forebodingly complex inferences: due to lack of knowledge about the global network structure, and unavailability of private observations, as well as third party interactions preceding every decision. Such difficulties make Bayesian updating of beliefs an implausible mechanism for social learning. To address these complexities, we consider a Bayesian without Recall model of inference. On the one hand, this model provides a tractable framework for analyzing the behavior of rational agents in social networks. On the other hand, this model also provides a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for the structure of the action space and utility functions for such agents and investigate the properties of learning, convergence, and consensus in special cases
Learning without Recall by Random Walks on Directed Graphs
We consider a network of agents that aim to learn some unknown state of the
world using private observations and exchange of beliefs. At each time, agents
observe private signals generated based on the true unknown state. Each agent
might not be able to distinguish the true state based only on her private
observations. This occurs when some other states are observationally equivalent
to the true state from the agent's perspective. To overcome this shortcoming,
agents must communicate with each other to benefit from local observations. We
propose a model where each agent selects one of her neighbors randomly at each
time. Then, she refines her opinion using her private signal and the prior of
that particular neighbor. The proposed rule can be thought of as a Bayesian
agent who cannot recall the priors based on which other agents make inferences.
This learning without recall approach preserves some aspects of the Bayesian
inference while being computationally tractable. By establishing a
correspondence with a random walk on the network graph, we prove that under the
described protocol, agents learn the truth exponentially fast in the almost
sure sense. The asymptotic rate is expressed as the sum of the relative
entropies between the signal structures of every agent weighted by the
stationary distribution of the random walk.Comment: 6 pages, To Appear in Conference on Decision and Control 201
Learning without Recall: A Case for Log-Linear Learning
We analyze a model of learning and belief formation in networks in which
agents follow Bayes rule yet they do not recall their history of past
observations and cannot reason about how other agents' beliefs are formed. They
do so by making rational inferences about their observations which include a
sequence of independent and identically distributed private signals as well as
the beliefs of their neighboring agents at each time. Fully rational agents
would successively apply Bayes rule to the entire history of observations. This
leads to forebodingly complex inferences due to lack of knowledge about the
global network structure that causes those observations. To address these
complexities, we consider a Learning without Recall model, which in addition to
providing a tractable framework for analyzing the behavior of rational agents
in social networks, can also provide a behavioral foundation for the variety of
non-Bayesian update rules in the literature. We present the implications of
various choices for time-varying priors of such agents and how this choice
affects learning and its rate.Comment: in 5th IFAC Workshop on Distributed Estimation and Control in
Networked Systems, (NecSys 2015
Distributed estimation and learning over heterogeneous networks
We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and quality of the observed data, as well as heterogeneity over time (intermittence). The goal of the studied aggregation schemes is to efficiently combine the observed data that is spread over time and across several network nodes, accounting for all the network heterogeneities. Moreover, we require no form of coordination beyond the local neighborhood of every network agent or sensor node. The three problems that we consider are (i) maximum likelihood estimation of the unknown given initial data sets, (ii) learning the true model parameter from streams of data that the agents receive intermittently over time, and (iii) minimum variance estimation of a complete sufficient statistic from several data points that the networked agents collect over time. In each case, we rely on an aggregation scheme to combine the observations of all agents; moreover, when the agents receive streams of data over time, we modify the update rules to accommodate the most recent observations. In every case, we demonstrate the efficiency of our algorithms by proving convergence to the globally efficient estimators given the observations of all agents. We supplement these results by investigating the rate of convergence and providing finite-time performance guarantees
Bayesian Heuristics for Group Decisions
We propose a model of inference and heuristic decision-making in groups that is rooted in the Bayes rule but avoids the complexities of rational inference in partially observed environments with incomplete information, which are characteristic of group interactions. Our model is also consistent with a dual-process psychological theory of thinking: the group members behave rationally at the initiation of their interactions with each other (the slow and deliberative mode); however, in the ensuing decision epochs, they rely on a heuristic that replicates their experiences from the first stage (the fast automatic mode). We specialize this model to a group decision scenario where private observations are received at the beginning, and agents aim to take the best action given the aggregate observations of all group members. We study the implications of the information structure together with the properties of the probability distributions which determine the structure of the so-called "Bayesian heuristics" that the agents follow in our model. We also analyze the group decision outcomes in two classes of linear action updates and log-linear belief updates and show that many inefficiencies arise in group decisions as a result of repeated interactions between individuals, leading to overconfident beliefs as well as choice-shifts toward extremes. Nevertheless, balanced regular structures demonstrate a measure of efficiency in terms of aggregating the initial information of individuals. These results not only verify some well-known insights about group decision-making but also complement these insights by revealing additional mechanistic interpretations for the group declension-process, as well as psychological and cognitive intuitions about the group interaction model
Learning from Neighbors about a Changing State
Agents learn about a changing state using private signals and past actions of
neighbors in a network. We characterize equilibrium learning and social
influence in this setting. We then examine when agents can aggregate
information well, responding quickly to recent changes. A key sufficient
condition for good aggregation is that each individual's neighbors have
sufficiently different types of private information. In contrast, when signals
are homogeneous, aggregation is suboptimal on any network. We also examine
behavioral versions of the model, and show that achieving good aggregation
requires a sophisticated understanding of correlations in neighbors' actions.
The model provides a Bayesian foundation for a tractable learning dynamic in
networks, closely related to the DeGroot model, and offers new tools for
counterfactual and welfare analyses.Comment: minor revision tweaking exposition relative to v5 - which added new
Section 3.2.2, new Theorem 2, new Section 7.1, many local revision