Difference between revisions of "Anvil problem"

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It has been pointed out by [[Eliezer Yudkowsky]] and others that [[AIXI]] does not model itself. AIXI is simply a calculation of the best possible action, extrapolating into the future, and at each step choosing the best action, which is calculated by recursively calculating the next step and so on into the horizon.  
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[[Eliezer Yudkowsky]] has [http://lesswrong.com/lw/om/qualitatively_confused/iqd pointed out] that "Both [[AIXI]] and AIXItl will at some point drop an anvil on their own heads just to see what happens..., because they are incapable of conceiving that any event whatsoever in the outside universe could change the computational structure of their own operations."
  
AIXI is very simple math. AIXI does not include a model of 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 or changed. This is not accurate for real-world implementations which may malfunction, self-modify, be destroyed, be changed, etc.
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[[AIXI]], the theoretical formalism for the most intelligent possible agent, does not model itself. It is simply a calculation of the best possible action, extrapolating into the future. This calculation  at each step chooses the best action, by recursively calculating the next step, and so on to the time horizon.
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AIXI is very simple math. AIXI does not consider its own structure in figuring 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 or changed. This is not accurate for real-world implementations which may malfunction, self-modify, be destroyed, be changed, etc.
  
 
Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could be changed or could change its behavior due to bugs. The AIXI formalism completely ignores these possibilities (Yampolskiy & Fox, 2012).
 
Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could be changed or could change its behavior due to bugs. The AIXI formalism completely ignores these possibilities (Yampolskiy & Fox, 2012).
  
This is called the [[Anvil problem]]: AIXI would not care if an anvil was about to drop on its head.
 
  
The "Anvil problem" is not a mere detail necessarily left out of a formalized abstraction. Self-analysis and self-modification are likely to be essential parts of any future [[Friendly AI]]. First, as the AI must strive to  avoid changes in its own goal system, the question of self-modeling cannot be ignored. Our decision theory must be improved to include [[Reflective decision theory|reflection]].  
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==Relevant to Friendly AI==
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AIXI is a valuable tool in theoretically considering the nature of super-intelligence, yet has its limitations. From one perspective, a self-model is a  mere detail necessarily left out of a formalized abstraction. Nonetheless, for researchers of a future [[Friendly AI|Friendly]] [[artificial general intelligence]], self-analysis and self-modification must be considered carefully. First, since any Friendly AI must strive to  avoid changes in its own goal system, the question of self-modeling cannot be ignored. Our decision theory must be improved to include [[Reflective decision theory|reflection]].  
  
 
Second, because human values are not well-understood or formalized, the FAI may need to refine its goal of maximizing human values. "Refining" the goal without changing its essentials is another demanding problem in reflective decision theory.  
 
Second, because human values are not well-understood or formalized, the FAI may need to refine its goal of maximizing human values. "Refining" the goal without changing its essentials is another demanding problem in reflective decision theory.  
  
Third, an FAI may choose to self-improve, to enhance its own intelligence to better achieve its goals. It may do so by altering its own implementation or by creating a new generation of AI, perhaps without regard for the destruction of the current implementation, so long as the new system can better achieve the goals. All these forms of self-modification again raise central questions about the self-model of the AI, which, as mentioned, is ignored by AIXI.
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Third, an artificial general intelligence will likely choose to self-improve, to enhance its own intelligence to better achieve its goals. It may do so by altering its own implementation, or by creating a new generation of AI. It may even do so without regard for the destruction of the current implementation, so long as the new system can better achieve the goals. All these forms of self-modification again raise central questions about the self-model of the AI, which, as mentioned, is not a part of AIXI.
  
 
==References==
 
==References==
  
 
[http://joshuafox.com/media/YampolskiyFox__AGIAndTheHumanModel.pdf 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.]
 
[http://joshuafox.com/media/YampolskiyFox__AGIAndTheHumanModel.pdf 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.]
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==Blog comment==
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[http://lesswrong.com/lw/om/qualitatively_confused/iqd Eliezer Yudkowsky] on  Qualitatively Confused at LessWrong, 15 March 2008.

Revision as of 02:47, 23 August 2012

Eliezer Yudkowsky has pointed out that "Both AIXI and AIXItl will at some point drop an anvil on their own heads just to see what happens..., because they are incapable of conceiving that any event whatsoever in the outside universe could change the computational structure of their own operations."

AIXI, the theoretical formalism for the most intelligent possible agent, does not model itself. It is simply a calculation of the best possible action, extrapolating into the future. This calculation at each step chooses the best action, by recursively calculating the next step, and so on to the time horizon.

AIXI is very simple math. AIXI does not consider its own structure in figuring 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 or changed. This is not accurate for real-world implementations which may malfunction, self-modify, be destroyed, be changed, etc.

Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could be changed or could change its behavior due to bugs. The AIXI formalism completely ignores these possibilities (Yampolskiy & Fox, 2012).


Relevant to Friendly AI

AIXI is a valuable tool in theoretically considering the nature of super-intelligence, yet has its limitations. From one perspective, a self-model is a mere detail necessarily left out of a formalized abstraction. Nonetheless, for researchers of a future Friendly artificial general intelligence, self-analysis and self-modification must be considered carefully. First, since any Friendly AI must strive to avoid changes in its own goal system, the question of self-modeling cannot be ignored. Our decision theory must be improved to include reflection.

Second, because human values are not well-understood or formalized, the FAI may need to refine its goal of maximizing human values. "Refining" the goal without changing its essentials is another demanding problem in reflective decision theory.

Third, an artificial general intelligence will likely choose to self-improve, to enhance its own intelligence to better achieve its goals. It may do so by altering its own implementation, or by creating a new generation of AI. It may even do so without regard for the destruction of the current implementation, so long as the new system can better achieve the goals. All these forms of self-modification again raise central questions about the self-model of the AI, which, as mentioned, is not a part of AIXI.

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.

Blog comment

Eliezer Yudkowsky on Qualitatively Confused at LessWrong, 15 March 2008.