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After reviewing extensive literature on the subject, Legg and Hutter summarizes the many possible valuable definitions in the informal statement “Intelligence measures an agent’s ability to achieve goals in a wide range of environments.” They then show this definition can be mathematically formalized given reasonable mathematical definitions of its terms. They use Solomonoff induction - a formalization of Occam's razor - to construct an universal artificial intelligence with a embedded utility function which assigns less utility to those actions based on theories with higher complexity. They argue this final formalization is a valid, meaningful, informative, general, unbiased, fundamental, objective, universal and practical definition of intelligence.
We can relate Legg and Hutter's definition with the concept of optimization. According to Eliezer Yudkowsky intelligence is efficient cross-domain optimization. It measures an agent's capacity for efficient cross-domain optimization of the world according to the agent’s preferences. Optimization measures not only the capacity to achieve the desired goal but also is inversely proportional to the amount of resources used. It’s the ability to steer the future so it hits that small target of desired outcomes in the large space of all possible outcomes, using fewer resources as possible. For example, when Deep Blue defeated Kasparov, it was able to hit that small possible outcome where it made the right order of moves given Kasparov’s moves from the very large set of all possible moves. In that domain, it was more optimal than Kasparov. However, Kasparov would have defeated Deep Blue in almost any other relevant domain, and hence, he is considered more intelligent.
One could cast this definition in a possible world vocabulary, intelligence is:
How many more worlds have a higher preference then the one realized by the agent, less intelligent he is. How many more worlds have a lower preference than the one realized by the agent, more intelligent he is. (Or: How much smaller is the set of worlds at least as preferable as the one realized, more intelligent the agent is). How much less paths for realizing the desired world using fewer resources than those spent by the agent, more intelligent he is. And finally, in how many more domains the agent can be more efficiently optimal, more intelligent he is. Restating it, the intelligence of an agent is directly proportional to:
and it is, accordingly, inversely proportional to:
This definition avoids several problems common in many others definitions, especially it avoids anthropomorphizing intelligence.