Anvil problem

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It has been pointed out by Eliezer Yudkowsky and others that AIXI lacks a self-model: It extrapolates its own actions into the future indefinitely, on the assumption that it will keep working in the same way in the future.

"AIXI does not 'model itself' to figure out what actions it will take in the future; implicit in its definition is the assumption that it will continue, up until its horizon, to choose actions that maximize expected future value. AIXI’s definition assumes that the maximizing action will always be chosen, despite the fact that the agent’s implementation was predictably destroyed. This is not accurate for real-world implementations which may malfunction, be destroyed, self-modify, etc

"Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could change its behavior due to bugs; and the AIXI formalism completely ignores these possibilities. This is called the Anvil problem: AIXI would not care if an anvil was about to drop on its head." (Yampolskiy, Fox, 2012).

References

R.V. Yampolskiy, J. Fox (2012) Artificial General Intelligence and the Human Mental Model. In Amnon H. Eden, Johnny Søraker, James H. Moor, Eric Steinhart (Eds.), The Singularity Hypothesis.The Frontiers Collection. London: Springer.