Are there approximate versions of the selection theorems? I haven’t seen anyone talk about them, but they might be easy to prove.
Approximate version of Kelly criteron: any agent that follows a strategy different by at least epsilon from Kelly betting will almost surely lose money compared to a Kelly-betting agent at a rate f(epsilon)
Approximate version of VNM: Any agent that satisfies some weakened version of the VNM axioms will have high likelihood under Boltzmann rationality (or some other metric of approximate utility maximization). The closest thing I’ve seen is logical inductors.
Approximate version of good regulator theorem: any approximately optimal regulator is equivalent to something that approximately models variables in its environment
Probably there are others.
Ideally, the assumptions and/or conclusions would describe how agents like humans, companies, animals, and ML systems actually work.
Are there approximate versions of the selection theorems? I haven’t seen anyone talk about them, but they might be easy to prove.
Approximate version of Kelly criteron: any agent that follows a strategy different by at least epsilon from Kelly betting will almost surely lose money compared to a Kelly-betting agent at a rate f(epsilon)
Approximate version of VNM: Any agent that satisfies some weakened version of the VNM axioms will have high likelihood under Boltzmann rationality (or some other metric of approximate utility maximization). The closest thing I’ve seen is logical inductors.
Approximate version of good regulator theorem: any approximately optimal regulator is equivalent to something that approximately models variables in its environment
Probably there are others.
Ideally, the assumptions and/or conclusions would describe how agents like humans, companies, animals, and ML systems actually work.