What do you think is the strongest argument for min-max over constant values for $1?
The constant $1 is the marginal current utility of the function, which is a reflection of its local properties only (very close utilities can have very different weightings), while min-max looks at its global properties.
The min-max is in expected utility given a policy, not in maximal utility that could happen, so it’s a bit less stupid than it would be in the second case.
1. In general there are diminishing returns to dollars, so global properties constrain local properties. (This is very true if you can gamble)
2. Your actual decisions mostly concern local changes, so it seems like a not-crazy thing to base your policy on.
That said, this proposal suffers from me making the same sign error as the (max-actual) proposal. Consider a theory with log utility in the number of dollars spent on it. As you spend less on it, its utility per dollar goes up and the weight goes down, so you further decrease the number of dollars, in the limit it has 0 dollars and infinite utility per dollar.
(It still seems like a sane approach for value learning, but not for moral uncertainty.)
The constant $1 is the marginal current utility of the function, which is a reflection of its local properties only (very close utilities can have very different weightings), while min-max looks at its global properties.
The min-max is in expected utility given a policy, not in maximal utility that could happen, so it’s a bit less stupid than it would be in the second case.
Well:
1. In general there are diminishing returns to dollars, so global properties constrain local properties. (This is very true if you can gamble)
2. Your actual decisions mostly concern local changes, so it seems like a not-crazy thing to base your policy on.
That said, this proposal suffers from me making the same sign error as the (max-actual) proposal. Consider a theory with log utility in the number of dollars spent on it. As you spend less on it, its utility per dollar goes up and the weight goes down, so you further decrease the number of dollars, in the limit it has 0 dollars and infinite utility per dollar.
(It still seems like a sane approach for value learning, but not for moral uncertainty.)