The paper presents some interesting ideas, but I think it ultimately fails to account for the fact that AGI does not mean "the ability of an agent to produce th

The paper presents some interesting ideas, but I think it ultimately fails to account for the fact that AGI does not mean "the ability of an agent to produce the absolute perfect solution to any problem", but rather "the ability of an agent to understand or learn any intellectual task that a human being can" (wiki for AGI, emphasis added). Taking that into account, in every example you provide I argue the human approach more closely aligns with the "limited" behavior the real-bound RL agent would demonstrate than the "perfect" approach a surreal RL agent might take. For instance: You argue a real-bound RL doctoring algorithm would not appropriately set "the patient dies" to `-Inf` weight, but in fact humans do not either. If we did you'd see in the case of a near-death patient absolutely every procedure, no matter how costly, experimental, dangerous, or irrelevant, would be attempted if it had even the slightest chance of increasing the likelihood of them not dying. In reality, doctors make risk-reward decisions on every patient, and will very often choose not to undertake costly, experimental, dangerous, or irrelevant procedures even if there is some documented minuscule chance of it working. Further, you argue that a real-bound RL theorem prover or composer would not know how to stop going down an ever increasing state-chain x_0, x_1, x_2, ... even if there existed some other state y that was "better" than any of the x's. But, this too is a very human behaviour! How many brilliant mathematicians, musicians, heck even software engineers, have spent their entire careers creating further and further derivatives of a known successful work, as opposed to starting anew and creating something truly world-changing? You also bring up a theoretical button which on every press gives you 1 point, versus a different button which gives infinite points on every power-of-two press. You argue that the real-bound RL agent would be forced to move to the 1-point-per-press button after some number of presses, but would any human really sit there pressing the button for all of eternity to eventually get the `Inf` instead of just saying "screw it I want something now"? Not to mention that the problem setup is fundamentally flawed, as within our current understanding of the universe there is no infinite supply of anything, and furthermore if there was an infinite supply of something you wouldn't have any benefit of pressing after the first press, much less waiting around for the billionth -- you'll continue to have an infinite supply. In fact, what you've done there is presumed a surreal universe by a) assuming that a button can provide an infinite supply of something, and b) assuming that having two of the infinities is better than having just one. So sure, if you're in a surreal universe, backing your RL with surreal numbers is a good idea. But we're, so far as I know, in a real universe, so backing with reals should be sufficient. Edit: I above use "surreal" to mean both the standard concept of surreal numbers in addition to any numbering concept which allows for and distinguishes between integer multiples of infinities.