In terms of state feedback, trial and error controls the knowledge state of the design in the designer’s head rather than the functional state of an embodied design in operation. With trial and error the designer learns. With true feedback control, the object does.
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Good diagnostic question to locate feedback loop: what is the living thing the loop passes through. If it’s a human the loop passes through, it’s trial and error. If the human could walk away and thing can autopilot in a changing environment for a while, there’s real feedback.
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There’s got to be a way to state this in a rigorous way. I think a trial-and-error loop is one that does not converge to a continuous transfer function in the limit of making the iteration interval smaller because there’s a process step that’s not bounded as function of step size
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Ie closed-loop assumes strongly bounded rationality in the feedback transfer function. You can do the e(t) —> u(t) computation in delta_t, as it goes to zero. Because e(t) gets smaller because stability.
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Human-in-the-loop is nearly the same as NP-hard problem solver in the loop, where the human can choose a particular good-enough heuristic solution in the time available. Ie, an agent that can change the problem when it can’t stretch the time. Ie a judging/valuing agent.
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Sorry, thinking out loud down a pseudo-mathematical bunnytrail. This is control theory geekery of as yet unclear relevance to practical things.
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Replying to @vgr
It looks like you are talking about the distinction between closed-loop and feedback policies. A classic paper by Bar-Shalom and Tse discusses this (CL policies are actively adaptive, incl. control of state uncertainty; FB policies are passively adaptive) https://www.mne.psu.edu/ray/ME(Math)577/me577_Bar-Shaloum1974.pdf …
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Replying to @mraginsky @vgr
Trial-and-error is closed-loop in this sense, because it has a dual effect in the sense of Feldbaum (taking actions influences your uncertainty about the future state): https://en.wikipedia.org/wiki/Dual_control_theory …
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Replying to @mraginsky
Hmm. I’m familiar with some later results in dual control around limits on the explore/exploit tradeoff. This definition is good, but I think I’m making a different distinction based on finite-time computability.
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Replying to @vgr
Yeah, there are tons of decidability and comp. complexity results surrounding control problems (discrete and continuous time), plus links to bounded rationality and RL. Lots of problems are NP-hard or even undecidable. So yeah, I can see this angle, hmmm.
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The problem is there is a genuine divide between most control theory, which is continuous time computation, and truly discrete systems. Discretization of continuous systems doesn’t quite bridge gap except in narrow classes. There is no proper computational understanding of former
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Replying to @vgr
There are some attempts (such as Branicky's), but, for the most part, I agree: there's no systematic treatment.https://www.sciencedirect.com/science/article/pii/030439759400147B …
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Replying to @mraginsky @vgr
Maxim Raginsky Retweeted Andrej Bauer
I am still trying to wrap my head around the leads in this thread:https://twitter.com/andrejbauer/status/1212737162732589056?s=20 …
Maxim Raginsky added,
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