Stuart_Armstrong comments on Versions of AIXI can be arbitrarily stupid - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (59)
Interesting paper, but I'm not sure this example is a good way to illustrate the result, since if someone actually built AIXI using the prior described in the OP, it will quickly learn that it's not in Hell since it won't actually receive ε reward for outputting "0".
Here's my attempt to construct a better example. Suppose you want to create an agent that qualifies as an AIXI but keeps just outputting "I am stupid" for a very long time. What you do is give it a prior which assigns ε weight to a "standard" universal prior, and rest of the weight to a Hell environment which returns exactly the same (distribution of) rewards and inputs as the "standard" prior for outputting "I am stupid." and 0 reward forever if the AIXI ever does anything else. This prior still qualifies as "universal".
This AIXI can't update away from its initial belief in the Hell environment because it keeps outputting "I am stupid" for which the Hell environment is indistinguishable from the real environment. If in the real world you keep punishing it (give it 0 reward), I think eventually this AIXI will do something else because its expected reward for outputting "I am stupid" falls below ε so risking almost certainty of the 0 reward forever of Hell for the ε chance of getting a better outcome becomes worthwhile. But if ε is small enough it may be impossible to punish AIXI consistently enough (i.e., it could occasionally get a non-zero reward due to cosmic rays or quantum tunneling) to make this happen.
I think one could construct similar examples for UDT so the problem isn't with AIXI's design, but rather that a prior being "universal" isn't "good enough" for decision making. We actually need to figure out what the "actual", or "right", or "correct" prior is. This seems to resolve one of my open problems.
The example was meant to show that if it was in Heaven, it will behave as if it was in Hell (now that's a theological point there ^_^ ). Your example is more general.
The result of the paper is that as long as the AIXI gets a minimum non-zero average reward (essentially), you can make it follow that policy forever.