No matter what the reward function, isn’t a rational maximizer engaging in repeated play going to “end up” concave due to e.g Kelly Criterion? I would think convex agents would be sub-optimal/quickly self-destruct if you tried to create one and nature will basically never do so.
Lots of people think that. Occasionally because they are in a situation where the assumptions of Kelly don’t hold (for example, you are not playing a repeated game), but more often because they confuse single bets (where Kelly maximizes log dollars) with repeated play (where Kelly maximizes total dollars).
In the long run, Kelly is optimal so long as your utility function is monotonic in dollars since it maximizes your total dollars.
Whether it is possible to justify Kelly betting even when your utility is linear in money (SBF said it was for him) is very much an open research problem. There are various posts on this topic when you search LessWrong for “Kelly”. I wouldn’t assume Wikipedia contains authoritative information on this question yet.
No matter what the reward function, isn’t a rational maximizer engaging in repeated play going to “end up” concave due to e.g Kelly Criterion? I would think convex agents would be sub-optimal/quickly self-destruct if you tried to create one and nature will basically never do so.
In what way would Kelly instruct you to be concave?
I think (not sure) Kelly Criterion applies to you only if you already are concave
Lots of people think that. Occasionally because they are in a situation where the assumptions of Kelly don’t hold (for example, you are not playing a repeated game), but more often because they confuse single bets (where Kelly maximizes log dollars) with repeated play (where Kelly maximizes total dollars).
In the long run, Kelly is optimal so long as your utility function is monotonic in dollars since it maximizes your total dollars.
From wikipedia
Whether it is possible to justify Kelly betting even when your utility is linear in money (SBF said it was for him) is very much an open research problem. There are various posts on this topic when you search LessWrong for “Kelly”. I wouldn’t assume Wikipedia contains authoritative information on this question yet.