Abstract
A direct implication of active inference, by way of minimizing expected free energy, is the ability to reframe optimization problems as they relate to biological systems. Instead of employing objective functions in order to maximizing an agent’s exposure to some exogenous measurable quantity, active inference describes how biological systems optimize by minimizing a divergence (KL) between a posterior probability density and a generative density, by definition endogenous to the system. This particular framework can be shown to underwrite many seemingly disparate disciplines in economics, and may prove to be a source of new insights for the field.
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Notes
- 1.
The observation that goods or services are preferred sooner rather than later, all else being equal. In economics, the prefixes “high” or “low” is sometimes used in order to differentiate between various levels of “impatience”. High time preference agents will value time at a high rate and display high levels of impatience, while low time preference agents will display low levels of impatience. High or low time preferences are therefor often used as explanations for various levels of propensities to consume or save in an economy.
- 2.
Revealed preferences is a way to infer an agents utility function by observing past behaviour. As such, agents cannot change their preferences once they have been revealed, since this would change the utility function and hereby greatly complicate economic modelling practices. The concept of revealed preferences is tightly linked to the transitivity axiom [18, 19].
- 3.
The idea, that in situations where optimal solutions do not exist, an agent will search until a solution is deemed to be good enough.
- 4.
There is at present no corollary in the economic literature to a rate of remuneration as used in this presentation. Normally a remuneration rate simply refers to a salary or stream of payments due for work or services rendered. Here, a rate of remuneration refers the expected energy input for a system given energy output, where the minimum requirement is long run homeostasis. For this reason the term may be ill conceived. Conversely, the term as used herein perfectly captures the observation, that agents have a preference for increasing over declining sequences not strictly “permissible” under a rational expectations framework [25, 26].
- 5.
Normally present value refers to the value at present of a discounted future cash flow where \(PV= \frac{CF}{{\left(1+r\right)}^{n}}\). Here, the term refers to subjective value given a time component. As such, it is the expected value of something that by necessity must lie in the future, and therefore must be discounted to some degree, considering a generative model that takes surprise or uncertainty into account. We can therefore also treat present value and utility (discounted) as interchangeable.
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Henriksen, M. (2021). Blankets All the Way up – the Economics of Active Inference. In: Kamp, M., et al. Machine Learning and Principles and Practice of Knowledge Discovery in Databases. ECML PKDD 2021. Communications in Computer and Information Science, vol 1524. Springer, Cham. https://doi.org/10.1007/978-3-030-93736-2_53
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