Boundedly-Rational Fast-Tuning Control Theory and Statistical Mechanics
We construct a model of control theory with "fast-tuning" of parameters related to the ambient dynamics of the system. The parameters are tuned ‘myopically’ (i.e., small changes are made), 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 the bounded rationality of the agent (s) tuning the parameters - that is, they may not follow the optimal path for tuning because of the lack of complete information about the system, errors in judgment, and / or a desire to experiment and test other options.
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