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Boundedly-Rational Fast-Tuning Control Theory and Statistical Mechanics

Michael J Campbell

posted on 26 August 2020

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We construct a model of control theory with 'fast-tuning' of parameters relative to the ambient dynamics of the system. The parameters are tuned 'myopically' (i.e., small changes are made), along with a random perturbation that allows for a large net change with certain probability. This is modeled using a drift-diffusion stochastic partial differential equation. The idea is to model 'bounded rationality' of the agent(s) tuning the parameters-that is, they may not follow the optimal path for tuning because of a lack of complete information about the system, errors in judgement, and/or a desire to experiment and test other options.