--- On Sun, 11/30/08, Philip Hunt <[EMAIL PROTECTED]> wrote: > Can someone explain AIXI to me?
AIXI models an intelligent agent interacting with an environment as a pair of interacting Turing machines. At each step, the agent outputs a symbol to the environment, and the environment outputs a symbol and a numeric reward signal to the agent. The goal of the agent is to maximize the accumulated reward. Hutter proved that the optimal solution is for the agent to guess, at each step, that the environment is simulated by the shortest program that is consistent with the interaction observed so far. Hutter also proved that the optimal solution is not computable because the agent can't know which of its guesses are halting Turing machines. The best it can do is pick numbers L and T, try all 2^L programs up to length L for T steps each in order of increasing length, and guess the first one that is consistent. If there are no matches, then it needs to choose larger L and T and try again. That solution is called AIXI^TL. It's time complexity is O(T 2^L). In general, it may require L up to the length of the observed interaction (because there is a fast program that outputs the agent's observations from a list of length L). In a separate paper ( http://www.vetta.org/documents/ui_benelearn.pdf ), Legg and Hutter propose defining universal intelligence as the expected reward of an AIXI agent in random environments. The value of AIXI is not that it solves the general intelligence problem, but rather it explains why the problem is so hard. It also justifies a general principle that is already used in science and in practical machine learning algorithms: to choose the simplest hypothesis that fits the data. It formally defines "simple" as the length of the shortest program that outputs a description of the hypothesis. For example, to avoid overfitting in neural networks, you should use the smallest number of connections and the least amount of training needed to fit the training data, then stop. In this case, the complexity of your neural network is the length of the shortest program that outputs the configuration of your network and its weights. Even if you don't know what that program is, and haven't chosen a programming language, you may reasonably expect that fewer connections, smaller weights, and coarser weight quantization will result in a shorter program. -- Matt Mahoney, [EMAIL PROTECTED] ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=120640061-aded06 Powered by Listbox: http://www.listbox.com
