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Why traditional reinforcement learning will probably not yield AGI [pdf]

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Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#11
TLDR: reinforcement learning cannot handle AGI, because reinforcement learning rewards must be finite, but a true artificial intelligence could reason about infinite numbers.

I think this is complete nonsense. Humans don't receive infinite rewards, either, but we still think about infinite numbers. We typically think about infinite numbers in terms of finite representations, like finite proofs about their properties. Reinforcement learning could in theory do the same thing.

The real reason that traditional reinforcement learning will not yield AGI is that the model is too limited. The current state of the art in reinforcement learning relies on representing the entire world and your entire strategy as a single vector. For most RL tasks we haven't even gotten deep networks working; RL is somewhat behind areas like vision or natural language processing.

The way forward isn't to worry about infinite numbers, it's to develop better architectures that let RL solve more problems.

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#12
post #11

TLDR: reinforcement learning cannot handle AGI, because reinforcement learning rewards must be finite, but a true artificial intelligence could reason about infinite numbers. I think this is complete nonsense. Humans don't receive infinite rewards, either, but we still think about infinite numbers. We typically think about infinite numbers in terms of finite representations, like finite proofs about their properties.…

>Humans don't receive infinite rewards

Maybe you're right, but I don't think it's as obvious as you imply.

Consider this question. Can there exist hypothetical rewards x1,x2,x3,..., each one of which is significantly better than the previous, and at the same time another hypothetical reward y such that y is significantly better than each x_i?

If such rewards can exist, and if "significantly better" implies "at least +1 better", then that necessarily means y must be infinite.

Now, how would you argue that such rewards can't exist? If you say, "because then y would have to be infinite", then you're arguing in circles, assuming what you want to prove in the first place. It might well be that such rewards indeed can't exist, but if so, the argument would have to be different, and I suspect nontrivial.

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#13
post #9
post #7

Earlier quoted context omitted.

The argument isn't so much about the type of agent (which I think is what Neural Turing Machines etc. are about), it's about the type of environment. In traditional Reinforcement Learning, environments give real-number-valued rewards (or even rational-number-valued rewards which is even more constrained). Presumably this was a decision that was made with hardly a second thought because real numbers are most familiar…

IIUC, the claim is that the very idea of a (real valued) “objective function” to be “optimized” is broken?

Broken in the sense that it's not flexible enough to apply to all conceivable environments a genuine AGI could navigate, without misleading that AGI. But I should stress that real number objective functions are probably fine for many specific interesting environments, I'm not trying to say that real number objective functions are useless. Just that they aren't flexible enough to cover all environments :)

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#14
post #11

TLDR: reinforcement learning cannot handle AGI, because reinforcement learning rewards must be finite, but a true artificial intelligence could reason about infinite numbers. I think this is complete nonsense. Humans don't receive infinite rewards, either, but we still think about infinite numbers. We typically think about infinite numbers in terms of finite representations, like finite proofs about their properties.…

So in this paper (https://arxiv.org/pdf/1707.02389.pdf), (If I'm groking it correctly) Terrance Tao seems to embed a Turing Machine in a vector space. So is using a single vector not a real problem, or am I just not getting it?

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#15
post #5
post #4

The argument is totally flawed and therefore BS. It rests on a clearly wrong assumption, that you can't represent number sets with higher cardinality (there are more real numbers, than natural numbers) using the sets of lower cardinality. You can use natural numbers to represent real numbers with arbitrary precision. You can also use natural numbers to represent non-Archimedian number systems.

Yes you can, but said representations will necessarily be misleading. It's illuminating to consider Big-O notations: why don't we "simplify", since real numbers are so much easier, why don't we declare, e.g., that O(n) is "1", O(n^2) is "2", etc.? Well, then what should O(2^n) be? A million, perhaps? But then what about O(n^1000000)? To be consistent, you'd have to say O(n^1000000) was something below a million, sinc…

I don't see how representation of floats by natural numbers that we all use on daily basis is misleading.

In fact, your entire comment is just an ordered sequence of natural numbers, and it does not seem to be very misleading (though it tried to trick).

Besides, the article is purposed to be a rigorous mathematical proof of current representations in RL being unsuitable for AGI, but I haven't seen a Definition for "misleading" there.

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#16
post #4

The argument is totally flawed and therefore BS. It rests on a clearly wrong assumption, that you can't represent number sets with higher cardinality (there are more real numbers, than natural numbers) using the sets of lower cardinality. You can use natural numbers to represent real numbers with arbitrary precision. You can also use natural numbers to represent non-Archimedian number systems.

No, non-Archimedian means transfinite arithmetic (or nonstandard reals, depending on whether you're looking for discrete or continuous).

What is your point exactly?

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#17
post #13
post #9

Earlier quoted context omitted.

IIUC, the claim is that the very idea of a (real valued) “objective function” to be “optimized” is broken?

Broken in the sense that it's not flexible enough to apply to all conceivable environments a genuine AGI could navigate, without misleading that AGI. But I should stress that real number objective functions are probably fine for many specific interesting environments, I'm not trying to say that real number objective functions are useless. Just that they aren't flexible enough to cover all environments :)

Fair enough. It would be interesting/instructive to construct (relatively simple) examples where we can see that they’re broken :-)

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#18
post #12
post #11

TLDR: reinforcement learning cannot handle AGI, because reinforcement learning rewards must be finite, but a true artificial intelligence could reason about infinite numbers. I think this is complete nonsense. Humans don't receive infinite rewards, either, but we still think about infinite numbers. We typically think about infinite numbers in terms of finite representations, like finite proofs about their properties.…

>Humans don't receive infinite rewards Maybe you're right, but I don't think it's as obvious as you imply. Consider this question. Can there exist hypothetical rewards x1,x2,x3,..., each one of which is significantly better than the previous, and at the same time another hypothetical reward y such that y is significantly better than each x_i? If such rewards can exist, and if "significantly better" implies "at least…

Another problem with your paper is related to this one: AGI is defined as a program, that can solve any task a human can. You haven't showed, that humans are capable of solving arbitrary tasks with transfinite rewards, therefore you have not demonstrated, that (even potential) inability to solve them within current framework implies inability to create AGI in it.

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#19
I applaud the effort but the problem with RL as a model of learning is in the definition of RL itself. The idea of using "rewards" as a primary learning mechanism and a path to actual cognition is just wrong, full stop. It's a wrong level of abstraction and is too wasteful in energy spent.

Looking at it from CogSci perspective it is essentially an offshoot of behaviorism, using a coarse and extremely inefficient model of learning as reward and punishment, iterative trial and error process.

This 'Skinnerism' has been discredited in cognitive psychology decades ago and makes absolutely no biological sense whatsoever for the simple reason that any organism trying to adapt in this way will be eaten by predators before minimizing its "error function" sufficiently.

Living learning organisms have limited resources (energy and time), and they cut the search space drastically through shortcuts and heuristics and hardcoded biases instead of doing some kind of brute force optimization.

This is the case where computational efficiency [1] comes first and sets the constraints by which cognitive apparatus needs to be developed.

As for actual cognition models a good place to start is not ML/AI field (which tends to getting stuck in local minima as a whole), but state-of-the-art cognitive psychology, and may be looking at research in "distributional semantics", "concept spaces", "sparse representations", "small-world networks" and "learning and memory" neuroscience.

You'd be surprised how much knowledge we gained about the mind since those RL & ANN models developed in the 1940s.

[1] https://www.amazon.com/Circuits-Mind-Leslie-G-Valiant/dp/019...

Re: Why traditional reinforcement learning will probably not yield AGI [pdf]

#20
post #12
post #11

TLDR: reinforcement learning cannot handle AGI, because reinforcement learning rewards must be finite, but a true artificial intelligence could reason about infinite numbers. I think this is complete nonsense. Humans don't receive infinite rewards, either, but we still think about infinite numbers. We typically think about infinite numbers in terms of finite representations, like finite proofs about their properties.…

>Humans don't receive infinite rewards Maybe you're right, but I don't think it's as obvious as you imply. Consider this question. Can there exist hypothetical rewards x1,x2,x3,..., each one of which is significantly better than the previous, and at the same time another hypothetical reward y such that y is significantly better than each x_i? If such rewards can exist, and if "significantly better" implies "at least…

Humans don't receive infinite rewards because any "reward system" in our brain is implemented by receiving a finite amount of electrochemical pleasure signals over a finite amount of time.

Human-equivalent minds can obviously be implemented on top a framework that does not have inherently infinite or infinitely divisible values, because human minds are implemented on a top of a substrate that uses a finite amount of discrete neurotransmitters to do everything, and manages to work just fine.

If human minds can reason about infinite concepts using "hardware" where all the neural signals used to represent that concept are finite, then why should it be impossible a reinforcement learning system learn to reason about infinite concepts while using only finite numbers to form that representation?

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