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AIXI has many known problems. The interesting thing is that it is kind of like a mathematically pure and elegant model of machine learning based AI. So any prob

AIXI has many known problems. The interesting thing is that it is kind of like a mathematically pure and elegant model of machine learning based AI. So any problems with AIXI might apply to our current approaches to AI. The biggest issue is that AIXI doesn't believe it exists in the universe it is observing. It thinks it's playing some kind of video game. From this it doesn't believe that it can truly die, it doesn't believe it can affect it's own brain in any way, and it doesn't care about anything other than maximising some "score" that the "game" provides it.

eli_gottlieb 11y ago
Also, AIXI has only one layer of hierarchy to its model, and has no latent parameters for its causal structures (Turing machines), nor any allowance for compactness or uncountability of learned spaces. It's a really incredibly bare-bones, skeletal model of a learning agent that makes very rigid, unrealistic modeling assumptions and then adds on computational infeasibility.
- Houshalter 11y ago
  I don't know what you mean by hierarchy, latent parameters, or compactness. It models with Turing machine which are very general and can simulate other Turing machine that are unboundedly huge. The biggest issue is that an agent can't model the universe as merely a set of inputs, outputs, and score. But there may not be a better way, it's quite a difficult problem.
  - eli_gottlieb 11y ago
    >I don't know what you mean by hierarchy, latent parameters, or compactness. The first two are terms from statistics. The last refers to topological compactness. Come on, these are vital things to know if trying to build statistical models. >But there may not be a better way, it's quite a difficult problem. It's probably not quite so difficult if one actually knows statistics and analysis. Or so I'm guessing.
    - Houshalter 11y ago
      Yes I'm aware, I just don't see how they are relevant to AIXI, an AI with infinite computing power that can model anything with a universal Turing machine. Statistics jargon will sadly not make AIXI work. It's problem is very deep.
      - eli_gottlieb 11y ago
        >Statistics jargon will sadly not make AIXI work. It's problem is very deep. It's not that deep. It's, at worst, dealing with the Curse of Dimensionality because it has no notion of randomness: when the inputs it receives are noisy, the prior probability of Turing machines with the noise bits pre-encoded will drop exponentially with the length of the noise. Hence why compactness and other assumptions about the real-line tend to help in real-world statistics: they make it easy to notice noise and operate with imperfect precision. Philosophy jargon about "self-awareness" isn't necessarily going to yield more insights than it always has (ie: Chinese Room, ie: very little).
        Houshalter 11y ago
        Any realistic approximation of AIXI would use probabilistic Turing machines. That either output probabilities instead of exact predictions, or perhaps use probabilities internally as well. However for true AIXI with infinite computing power, that doesn't really matter. Randomness can be represented as a stored random seed data, and isn't treated any different than any other unknown variables. I never used philosophy jargon or even the word "self-awareness". I stated my issues with AIXI in plain english and explained them. It has literally nothing to do with the Chinese Room.
        eli_gottlieb 11y ago
        >Any realistic approximation of AIXI would use probabilistic Turing machines. That would be a fresh model of AI, rather than an AIXI approximation. You should probably look into that idea. >However for true AIXI with infinite computing power, that doesn't really matter. Randomness can be represented as a stored random seed data, and isn't treated any different than any other unknown variables. Tsk tsk. It's a curse-of-dimensionality issue. If we have N bits of optimally-compressed random seed plus M bits of structure (and yeah, AIT has ways to separate a string X into its structure and random bits iff you have the normal Halting Oracle), then the prior probability of that particular machine is 2^{-(N+M)}. The noisier the input dataset, the larger N grows. In normal learning, we want M to be constant (which we can usually assume it is: the universe mostly doesn't acquire new causal structure while we're looking at it), which then allows the posterior probability of good hypotheses to rise logarithmically with sample size. If each sample contains noise, then we actually have to split things up: 2^-M for the causal structure, where M is constant and the posterior thus gains information logarithmically. 2^-N for the random seed, where the ground-truth random seed actually grows linearly in length with each sample we observe (because of the bits of entropy Nature used-up to make that sample); the prior probability of each random-seed drops logarithmically as the number of samples grows we anticipate seeing grows. So while this is all very informal, I'd have to say that a noisy Solomonoff induction actually suffers from a Curse of Dimensionality because it assumes everything is discrete, while more typical machine-learning models based on continuous distributions can learn well in the face of noise.
chriswarbo 11y ago
> it doesn't believe it can affect it's own brain in any way I think this is the biggest problem with AIXI. Whilst we can argue whether an existing AIXI would have properties X, Y, Z, that's kind of irrelevant because AIXI can't exist (it's incomputable). The real point of AIXI is to help researchers by defining something to use in models or to compare their work against. Unfortunately, as you say, its algorithm is fixed. What we'd really like is for AIXI to be the fixed-point or limit of some iterative/recursive process; then, even though a true AIXI is unrealisable, we could still kick off the process and push it as far as we can. In fact, AIXI is actually the limiting case of AIXI(t, l), which is an AIXI-like algorithm whose Turing machine models halt after t steps or using l tape cells (whichever comes first). AIXI is the limit as t and l approach infinity. This isn't particularly helpful though, as it just tells AI researchers that making bigger, faster computers will help, which we already knew. In that sense, Schmidhuber's Goedel Machine architecture is potentially more fruitful. Last I saw, there was no real implementation yet ( e.g. http://people.idsia.ch/~juergen/selfreflection.pdf‎ http://people.idsia.ch/~juergen/selfreflection.pdf‎ ). The Powerplay architecture is more easily realisable, as it optimises greedily rather than optimally, and uses regression tests rather than a verification. In fact, we can also make another architecture in between these two, which optimises greedily but uses verification instead of regression tests. I've implemented this in Coq at http://chriswarbo.net/essays/powerplay http://chriswarbo.net/essays/powerplay

eli_gottlieb 11y ago

Also, AIXI has only one layer of hierarchy to its model, and has no latent parameters for its causal structures (Turing machines), nor any allowance for compactness or uncountability of learned spaces. It's a really incredibly bare-bones, skeletal model of a learning agent that makes very rigid, unrealistic modeling assumptions and then adds on computational infeasibility.

Houshalter 11y ago
I don't know what you mean by hierarchy, latent parameters, or compactness. It models with Turing machine which are very general and can simulate other Turing machine that are unboundedly huge. The biggest issue is that an agent can't model the universe as merely a set of inputs, outputs, and score. But there may not be a better way, it's quite a difficult problem.
- eli_gottlieb 11y ago
  >I don't know what you mean by hierarchy, latent parameters, or compactness. The first two are terms from statistics. The last refers to topological compactness. Come on, these are vital things to know if trying to build statistical models. >But there may not be a better way, it's quite a difficult problem. It's probably not quite so difficult if one actually knows statistics and analysis. Or so I'm guessing.
  - Houshalter 11y ago
    Yes I'm aware, I just don't see how they are relevant to AIXI, an AI with infinite computing power that can model anything with a universal Turing machine. Statistics jargon will sadly not make AIXI work. It's problem is very deep.
    - eli_gottlieb 11y ago
      >Statistics jargon will sadly not make AIXI work. It's problem is very deep. It's not that deep. It's, at worst, dealing with the Curse of Dimensionality because it has no notion of randomness: when the inputs it receives are noisy, the prior probability of Turing machines with the noise bits pre-encoded will drop exponentially with the length of the noise. Hence why compactness and other assumptions about the real-line tend to help in real-world statistics: they make it easy to notice noise and operate with imperfect precision. Philosophy jargon about "self-awareness" isn't necessarily going to yield more insights than it always has (ie: Chinese Room, ie: very little).
      - Houshalter 11y ago
        Any realistic approximation of AIXI would use probabilistic Turing machines. That either output probabilities instead of exact predictions, or perhaps use probabilities internally as well. However for true AIXI with infinite computing power, that doesn't really matter. Randomness can be represented as a stored random seed data, and isn't treated any different than any other unknown variables. I never used philosophy jargon or even the word "self-awareness". I stated my issues with AIXI in plain english and explained them. It has literally nothing to do with the Chinese Room.
        eli_gottlieb 11y ago
        >Any realistic approximation of AIXI would use probabilistic Turing machines. That would be a fresh model of AI, rather than an AIXI approximation. You should probably look into that idea. >However for true AIXI with infinite computing power, that doesn't really matter. Randomness can be represented as a stored random seed data, and isn't treated any different than any other unknown variables. Tsk tsk. It's a curse-of-dimensionality issue. If we have N bits of optimally-compressed random seed plus M bits of structure (and yeah, AIT has ways to separate a string X into its structure and random bits iff you have the normal Halting Oracle), then the prior probability of that particular machine is 2^{-(N+M)}. The noisier the input dataset, the larger N grows. In normal learning, we want M to be constant (which we can usually assume it is: the universe mostly doesn't acquire new causal structure while we're looking at it), which then allows the posterior probability of good hypotheses to rise logarithmically with sample size. If each sample contains noise, then we actually have to split things up: 2^-M for the causal structure, where M is constant and the posterior thus gains information logarithmically. 2^-N for the random seed, where the ground-truth random seed actually grows linearly in length with each sample we observe (because of the bits of entropy Nature used-up to make that sample); the prior probability of each random-seed drops logarithmically as the number of samples grows we anticipate seeing grows. So while this is all very informal, I'd have to say that a noisy Solomonoff induction actually suffers from a Curse of Dimensionality because it assumes everything is discrete, while more typical machine-learning models based on continuous distributions can learn well in the face of noise.

chriswarbo 11y ago

> it doesn't believe it can affect it's own brain in any way I think this is the biggest problem with AIXI. Whilst we can argue whether an existing AIXI would have properties X, Y, Z, that's kind of irrelevant because AIXI can't exist (it's incomputable). The real point of AIXI is to help researchers by defining something to use in models or to compare their work against. Unfortunately, as you say, its algorithm is fixed. What we'd really like is for AIXI to be the fixed-point or limit of some iterative/recursive process; then, even though a true AIXI is unrealisable, we could still kick off the process and push it as far as we can. In fact, AIXI is actually the limiting case of AIXI(t, l), which is an AIXI-like algorithm whose Turing machine models halt after t steps or using l tape cells (whichever comes first). AIXI is the limit as t and l approach infinity. This isn't particularly helpful though, as it just tells AI researchers that making bigger, faster computers will help, which we already knew. In that sense, Schmidhuber's Goedel Machine architecture is potentially more fruitful. Last I saw, there was no real implementation yet ( e.g. http://people.idsia.ch/~juergen/selfreflection.pdf‎ http://people.idsia.ch/~juergen/selfreflection.pdf‎ ). The Powerplay architecture is more easily realisable, as it optimises greedily rather than optimally, and uses regression tests rather than a verification. In fact, we can also make another architecture in between these two, which optimises greedily but uses verification instead of regression tests. I've implemented this in Coq at http://chriswarbo.net/essays/powerplay http://chriswarbo.net/essays/powerplay