73,105 research outputs found
AGREEING TO DISAGREE: A SURVEY
Aumann (1976) put forward a formal definition of common knowledge and used it to prove that two ""like minded"" individuals cannot ""agree to disagree"" in the following sense. If they start from a common prior and update the probability of an event E (using Bayes'' rule) on the basis of private information, then it cannot be common knowledge between them that individual 1 assigns probability p to E and individual 2 assigns probability q to E with p ¹ q. In other words, if their posteriors of event E are common knowledge then they must coincide. Aumann''s Agreement Theorem has given rise to a large literature which we review in this paper. The results are classified according to whether they are probabilistic (Bayesian) or qualitative. Particular attention is paid to the issue of how to interpret the notion of Harsanyi consistency as a (local) property of belief hierarchies.
Tracking probabilistic truths: a logic for statistical learning
We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds (or more generally, truth in all the worlds that are plausible enough). We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: (1) learning observable evidence obtained by repeated sampling from the unknown distribution; and (2) learning higher-order information about the distribution. The first changes only the plausibility map (via a ‘plausibilistic’ version of Bayes’ Rule), but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions (safe belief and statistical knowledge), as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense (statistical) knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning.publishedVersio
Technical Report: Cooperative Multi-Target Localization With Noisy Sensors
This technical report is an extended version of the paper 'Cooperative
Multi-Target Localization With Noisy Sensors' accepted to the 2013 IEEE
International Conference on Robotics and Automation (ICRA).
This paper addresses the task of searching for an unknown number of static
targets within a known obstacle map using a team of mobile robots equipped with
noisy, limited field-of-view sensors. Such sensors may fail to detect a subset
of the visible targets or return false positive detections. These measurement
sets are used to localize the targets using the Probability Hypothesis Density,
or PHD, filter. Robots communicate with each other on a local peer-to-peer
basis and with a server or the cloud via access points, exchanging measurements
and poses to update their belief about the targets and plan future actions. The
server provides a mechanism to collect and synthesize information from all
robots and to share the global, albeit time-delayed, belief state to robots
near access points. We design a decentralized control scheme that exploits this
communication architecture and the PHD representation of the belief state.
Specifically, robots move to maximize mutual information between the target set
and measurements, both self-collected and those available by accessing the
server, balancing local exploration with sharing knowledge across the team.
Furthermore, robots coordinate their actions with other robots exploring the
same local region of the environment.Comment: Extended version of paper accepted to 2013 IEEE International
Conference on Robotics and Automation (ICRA
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