Ben, Thanks for the comments on my RSI paper. To address your comments, 1. I defined "improvement" as achieving the same goal (utility) in less time or achieving greater utility in the same time. I don't understand your objection that I am ignoring run time complexity.
2. I agree that an AIXI type interactive environment is a more appropriate model than a Turing machine receiving all of its input at the beginning. The problem is how to formally define improvement in a way that distinguishes it from learning. I am open to suggestions. To see why this is a problem, consider an agent that after a long time, guesses the environment's program and is able to achieve maximum reward from that point forward. The agent could "improve" itself by hard-coding the environment's program into its successor and thereby achieve maximum reward right from the beginning. 3. A computer's processor speed and memory have no effect on the algorithmic complexity of a program running on it. -- Matt Mahoney, [EMAIL PROTECTED] --- On Mon, 10/13/08, Ben Goertzel <[EMAIL PROTECTED]> wrote: From: Ben Goertzel <[EMAIL PROTECTED]> Subject: Re: [agi] Updated AGI proposal (CMR v2.1) To: agi@v2.listbox.com Date: Monday, October 13, 2008, 8:33 PM Hi, OK, I read the supposed refutation of recursive self-improvement at http://www.mattmahoney.net/rsi.html There are at least three extremely major problems with the argument. 1) By looking only at algorithmic information (defined in terms of program length) and ignoring runtime complexity, you are ignoring much of the value to be achieved via RSI. Suppose program P1 can solve problems of class C and size 500 in 3 hours per problem. Then, suppose P1 spends 50 hours transforming itself into a new program,P2, that can solve problems of class C and size 500 in one second per problem. Furthermore, suppose the RAM available in the machine at hand cannot hold bothP1 and P2 at the same time. In this case, it's obvious there's a huge advantage involved in P1 replacing itself withP2 ... if solving problems of class C is important for P1 achieving its goals, and if P2 is oriented toward achieving the same goal. Your argument is blind to this advantage because it ignores runtime complexity. Your argument is fixated on the fact that P2 can be generated by information consistingof {P1 plus the data P1 has observed} ... but so what? Program length is not, initself, all that useful thing to be looking at in the context of real-world computing. We need to be thinking about both space and time complexity. 2) You don't consider the program as interacting with an environment. IMO you shouldbe using the mathematical setup that Hutter uses in his main theorems about AIXI and AIXItl. In this setup, the AI is an agent that takes actions in an environment, which then responds to its actions. Furthermore, you should enhance Hutter's setup to consider the case where the agenthas not only fixed RAM (together potentially with a larger amount of memory that is slower to access), but also has processing cycle that is defined in terms of the "cycle time" of the environment, so that it only gets N internal processing cycles per each opportunity to sense/act. Considering the argument in this kind of more realistic setting, the critical importance of runtime as I noted above would immediately become apparent. 3) You don't consider that a smarter program might be able to figure out ways to increase its processor speed or RAM capacity, thus breaking your theoretical assumptions altogether. In this case, P2 could have an arbitrarily larger algorithmic information than P1, contradicting your result (by using a different, more realistic assumption). ... In short, what you have shown is that, according to an uninteresting measure (algorithmic information), RSI is not very dramatically useful in an artificial situation (no environment, no restrictions on processor cycle consumption, no ability for intelligence to lead to hardware modification). -- Ben G ------------------------------------------- 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=117534816-b15a34 Powered by Listbox: http://www.listbox.com
