"Bringing all these pieces together, we can now define our formal measure of intelligence for arbitrary systems. Let E be the space of all computable reward summable environmental measures with respect to the reference machine U, and let K be the Kolmogorov complexity function. The expected performance of agent π with respect to the universal distribution 2−K(μ) over the space of all environments E is given by Υ(π) := [unquotable latex expression]. We call this the universal intelligence of agent π."
It is an useless kind of mathematical object from any practical perspective. Sure, some formal object is defined, but all the actual important things to use it are left as difficult, possibly devilishly or impossibly difficult implementation details. How do you actually build a map from the physical reality to environment E? How the agent π is mapped to any real physical being? All the real work that would make the definition useful is left out.
It is like defining complexity classes without providing any algorithms.
edit. Further complaint: Here is how they present "examples":
>A very specialised agent. From the equation for Υ, we see that an agent could have very low universal intelligence but still perform extremely well at a few very specific and
complex tasks. Consider, for example, IBM’s Deep Blue chess supercomputer, which we will represent by π_dblue. When μ_chess describes the game of chess, V π_dblue μ_chess is very high. However 2−K(μ_chess ) is small, and for μ != μ_chess the value function will be low as π_dblue only plays chess. Therefore, the value of Υ(π_dblue) will be very low. Intuitively, this is because Deep Blue is too inflexible and narrow to have general intelligence; a characteristic
weakness of specialised artificial intelligence systems.
Why they need any formal definition of Y to express this if they don't bother fleshing out some features of μ_chess so that you could provide any bounds for K(μ_chess)? Without such work, all of the actual claims in the paragraph is all appeal to intuition. Nothing is proved, so any formal definitions are unused. The contents of the quoted paragraph could be expressed without referring to any equations or "definitions" at all, they are totally superfluous.
"Bringing all these pieces together, we can now define our formal measure of intelligence for arbitrary systems. Let E be the space of all computable reward summable environmental measures with respect to the reference machine U, and let K be the Kolmogorov complexity function. The expected performance of agent π with respect to the universal distribution 2−K(μ) over the space of all environments E is given by Υ(π) := [unquotable latex expression]. We call this the universal intelligence of agent π."
It is an useless kind of mathematical object from any practical perspective. Sure, some formal object is defined, but all the actual important things to use it are left as difficult, possibly devilishly or impossibly difficult implementation details. How do you actually build a map from the physical reality to environment E? How the agent π is mapped to any real physical being? All the real work that would make the definition useful is left out.
It is like defining complexity classes without providing any algorithms.
edit. Further complaint: Here is how they present "examples":
>A very specialised agent. From the equation for Υ, we see that an agent could have very low universal intelligence but still perform extremely well at a few very specific and complex tasks. Consider, for example, IBM’s Deep Blue chess supercomputer, which we will represent by π_dblue. When μ_chess describes the game of chess, V π_dblue μ_chess is very high. However 2−K(μ_chess ) is small, and for μ != μ_chess the value function will be low as π_dblue only plays chess. Therefore, the value of Υ(π_dblue) will be very low. Intuitively, this is because Deep Blue is too inflexible and narrow to have general intelligence; a characteristic weakness of specialised artificial intelligence systems.
Why they need any formal definition of Y to express this if they don't bother fleshing out some features of μ_chess so that you could provide any bounds for K(μ_chess)? Without such work, all of the actual claims in the paragraph is all appeal to intuition. Nothing is proved, so any formal definitions are unused. The contents of the quoted paragraph could be expressed without referring to any equations or "definitions" at all, they are totally superfluous.