Reading this, I figured you were talking about local-descent-type optimization algorithms, i.e. gradient descent and variants.
From that perspective, there’s two really important pieces missing from these analogies:
The mountaineers can presumably backtrack, at least as long as the water remains low enough
The mountaineers can presumably communicate
With backtracking, even a lone mountaineer can do better sometimes (and never any worse) by continuing to explore after reaching the top of a hill—as long as he keeps an eye on the water, and makes sure he has time to get back. In an algorithmic context, this just means keeping track of the best point seen, while continuing to explore.
With backtracking and communication, the mountaineers can each go explore independently, then all come back and compare notes (again keeping track of water etc), all go to the highest point found, and maybe even repeat that process. In an algorithmic context, this just means spinning off some extra threads, then taking the best result found by any of them.
In an evolutionary context, those pieces are probably not so relevant.
Yes, those two pieces can change the situation dramatically (and I have tried writing another parable including them, but found it a bit difficult for me)
I’m pondering about what is the best strategy with communication. Initially I thought I can spread them out and each mountaineer knows the location/height of other mountaineers in a given radius (significantly larger than the visibility in the fog) and add that information into their “move towards the greatest height” algorithm. Which might work, but I cannot vigorously show how useful that will be.
Regardless, I think evolution can’t get much better than the third scenario, it doesn’t seem to backtrack and most likely doesn’t communicate.
There is also that my analogy fails to consider that the “environment” changes overtime, so the “mountain landscape” will not stay the same when you come back to a place after leaving it. This probably prevents backtracking, but doesn’t change the outcome that you’d most likely be stuck on a hilltop that isn’t the optimal.
The environment may change over time, but 1) mountains change slowly, and 2) that’s what brains are for. Even if “evolution doesn’t pick up on it”, how much will the height of a mountain (and which mountain is the tallest) naturally change over the course of your lifetime?
Reading this, I figured you were talking about local-descent-type optimization algorithms, i.e. gradient descent and variants.
From that perspective, there’s two really important pieces missing from these analogies:
The mountaineers can presumably backtrack, at least as long as the water remains low enough
The mountaineers can presumably communicate
With backtracking, even a lone mountaineer can do better sometimes (and never any worse) by continuing to explore after reaching the top of a hill—as long as he keeps an eye on the water, and makes sure he has time to get back. In an algorithmic context, this just means keeping track of the best point seen, while continuing to explore.
With backtracking and communication, the mountaineers can each go explore independently, then all come back and compare notes (again keeping track of water etc), all go to the highest point found, and maybe even repeat that process. In an algorithmic context, this just means spinning off some extra threads, then taking the best result found by any of them.
In an evolutionary context, those pieces are probably not so relevant.
Yes, those two pieces can change the situation dramatically (and I have tried writing another parable including them, but found it a bit difficult for me)
I’m pondering about what is the best strategy with communication. Initially I thought I can spread them out and each mountaineer knows the location/height of other mountaineers in a given radius (significantly larger than the visibility in the fog) and add that information into their “move towards the greatest height” algorithm. Which might work, but I cannot vigorously show how useful that will be.
Regardless, I think evolution can’t get much better than the third scenario, it doesn’t seem to backtrack and most likely doesn’t communicate.
There is also that my analogy fails to consider that the “environment” changes overtime, so the “mountain landscape” will not stay the same when you come back to a place after leaving it. This probably prevents backtracking, but doesn’t change the outcome that you’d most likely be stuck on a hilltop that isn’t the optimal.
The environment may change over time, but 1) mountains change slowly, and 2) that’s what brains are for. Even if “evolution doesn’t pick up on it”, how much will the height of a mountain (and which mountain is the tallest) naturally change over the course of your lifetime?