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  Non-Equilibrium Relations for Bounded Rational Decision-Making in Changing Environments

Grau-Moya, J., Krüger, M., & Braun, D. (2018). Non-Equilibrium Relations for Bounded Rational Decision-Making in Changing Environments. Entropy, 20(1): 1, pp. 1-28. doi:10.3390/e20010001.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0001-7D3B-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0001-80EB-5
Genre: Journal Article

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Grau-Moya, J1, 2, Author              
Krüger, M, Author
Braun, DA1, 2, Author              
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1Research Group Sensorimotor Learning and Decision-Making, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497809              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794              

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 Abstract: Living organisms from single cells to humans need to adapt continuously to respond to changes in their environment. The process of behavioural adaptation can be thought of as improving decision-making performance according to some utility function. Here, we consider an abstract model of organisms as decision-makers with limited information-processing resources that trade off between maximization of utility and computational costs measured by a relative entropy, in a similar fashion to thermodynamic systems undergoing isothermal transformations. Such systems minimize the free energy to reach equilibrium states that balance internal energy and entropic cost. When there is a fast change in the environment, these systems evolve in a non-equilibrium fashion because they are unable to follow the path of equilibrium distributions. Here, we apply concepts from non-equilibrium thermodynamics to characterize decision-makers that adapt to changing environments under the assumption that the temporal evolution of the utility function is externally driven and does not depend on the decision-maker’s action. This allows one to quantify performance loss due to imperfect adaptation in a general manner and, additionally, to find relations for decision-making similar to Crooks’ fluctuation theorem and Jarzynski’s equality. We provide simulations of several exemplary decision and inference problems in the discrete and continuous domains to illustrate the new relations.

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 Dates: 2018-01
 Publication Status: Published in print
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 Identifiers: DOI: 10.3390/e20010001
BibTex Citekey: GrauMoyaKB2018
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Title: Entropy
Source Genre: Journal
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Pages: - Volume / Issue: 20 (1) Sequence Number: 1 Start / End Page: 1 - 28 Identifier: -