Information Structures, the Witsenhausen Counterexample, and Communicating Using Actions

Grover, Pulkit

doi:10.1007/978-1-4471-5102-9_148-1

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…A book length treatment of the intrinsic model is given in (Carpentier et al, 2015). The intrinsic model continues to be studied (Grover, 2015;Nayyar et al, 2011Nayyar et al, , 2013Nayyar and Teneketzis, 2019;Nayyar and Basar, 2012), and was recently shown to generalize Pearl's causal do-calculus (Heymann et al, 2021).…”

Section: Information Fieldsmentioning

confidence: 99%

Universal Decision Models

Mahadevan¹

2021

Preprint

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Humans are universal decision makers: we reason causally to understand the world; we act competitively to gain advantage in commerce, games, and war; and we are able to learn to make better decisions through trial and error. Whilst these individual modalities of decision making have been studied for decades in various subfields of AI and ML, there has been commensurately less effort in developing formalisms that unify these various modalities into common framework. In this paper, we propose Universal Decision Model (UDM), a mathematical formalism based on category theory, to address this challenge. Decision objects in a UDM correspond to instances of decision tasks, ranging from causal models and dynamical systems such as Markov decision processes and predictive state representations, to network multiplayer games and Witsenhausen's intrinsic models, which generalizes all these previous formalisms. A UDM is a category of objects, which include decision objects, observation objects, and solution objects. Bisimulation morphisms map between decision objects that capture structure-preserving abstractions. We formulate universal properties of UDMs, including information integration, decision solvability, and hierarchical abstraction. Information integration consolidates data from heterogeneous sources by forming products or limits in the UDM category. Abstraction simulates complex decision processes by simpler processes through bisimulation morphisms by forming quotients, co-products and co-limits in the UDM category. Finally, solvability of a UDM decision object is defined by a fixed point equation, and it corresponds to an isotonic order-preserving morphism across the topology induced by UDM objects. We describe universal functorial representations of UDMs, and propose an algorithm for computing the minimal object in a UDM using algebraic topology. We sketch out an application of UDMs to causal inference in network economics, using a complex multiplayer producer-consumer two-sided marketplace.

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Section: Information Fieldsmentioning

confidence: 99%

Universal Decision Models

Mahadevan¹

2021

Preprint

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Feedback control goes wireless

Mager

Baumann²,

Jacob

et al. 2019

Proceedings of the 10th ACM/IEEE International Conference on Cyber-Physical Systems

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Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals of tens of milliseconds. Lowpower wireless technology is preferred for its low cost, small form factor, and flexibility, especially if the devices support multi-hop communication. So far, however, feedback control over wireless multi-hop networks has only been shown for update intervals on the order of seconds. This paper presents a wireless embedded system that tames imperfections impairing control performance (e.g., jitter and message loss), and a control design that exploits the essential properties of this system to provably guarantee closed-loop stability for physical processes with linear time-invariant dynamics. Using experiments on a cyber-physical testbed with 20 wireless nodes and multiple cart-pole systems, we are the first to demonstrate and evaluate feedback control and coordination over wireless multi-hop networks for update intervals of 20 to 50 milliseconds. CCS CONCEPTS• Computer systems organization → Sensors and actuators; Embedded systems; Real-time system architecture; Dependable and fault-tolerant systems and networks; • Networks → Cyber-physical networks; Network protocol design.

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Information Structures, the Witsenhausen Counterexample, and Communicating Using Actions

Cited by 2 publications

References 22 publications

Universal Decision Models

Universal Decision Models

Feedback control goes wireless

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