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by repsilat
2493 days ago
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There are certainly cases of weird degenerate solutions to optimization problems. Lots of examples in machine learning (one classic at https://openai.com/blog/faulty-reward-functions/). In more old-school convex optimization the closest thing is probably insufficiently constrained problems. If you don't say the amount of each food you eat has to be greater than zero, you can get all your dietary needs satisfied for the low low price of minus infinity dollars! From another perspective, though, perhaps there's a "No True Scotsman" side of this. Is a utility monster a sign of a badly-specified problem, or are they a definitive sign of one? If the former, it stands to reason it's not a "concern" for modellers -- it's a dream! |
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For example, the special "Felix" case ignores the case where said guy is stuck by gamma radiation and dies. Over time, the probability of that k or a bunch of other catastrophes ruinning the solution tends to 1.
Therefore, the best solution avoids the most known catastrophes and is updated as new possibilities of those are found. (Tontine lotto, anyone?) Minimax loss optimal. Maximin (maximizing gain without increasing base loss) could be decent as well. Deciding between the two is better left to wizards.
Online stochastic optimization is mathematical black magic anyway so far.
But then, satisfying humans is much easier given all the built in biases we have. Keeping things alive long term is much harder.