optimization tools?

[joel-becker]

i want to do something like this

budget = 1000 to 2000
utils_project_1(budget) = {budget ^ 0.5}
utils_project_2(budget) = {log(budget)}
utils_project_3(budget) = {0.01 * budget ^ 2}

then find a budget allocation across projects that maximizes utils.

i assume that numerical optimization tools are not yet supported in squiggle? i do have some vague recollection that @NunoSempere had a hacky solution to this some time ago. either way, some way to solve this problem would be great!

[berekuk]

Nuño's solution, Danger.optimalAllocationGivenDiminishingMarginalReturnsForManyFunctions, is still in Squiggle stdlib.

Here's an example: https://www.squiggle-language.com/playground?v=0.9.3#code=eNptj8FOwzAQRH9llZMt0uCk6gUJJERVTr1wxVCZxAlGzjpy7Kqoyb9jE5DA6mk9u29GnnPWyFZ47R5MI7Ob7M03nXRwCyVjDJyBKkyO3ik9HgZrPmTtDiVZMBq4H8MrsGKTctUfTpvuV6XY%2BlJcxZFjI606CqeOkrQ5yGGMyHk6TUBacoKrZbWCICiF6yjn6NsK7KQtzOBUL%2FS91qYOKQYfQxJuVa9Qje8Ku72wnUKhn6TzFsedsXuBnzuPdaRHwhHgOemeQ1IyXaxfog1gdQe9GMgiIHy7neB%2FIVaUdF7uNI%2Bz3DD2%2FQgXjjSbvwCOw4zb

Important:

• you'll have to use derivatives (functions that return marginal returns, not total returns) - easy to implement, see my example
• functions should be decreasing; your utils_project_3 doesn't satisfy that requirement, so the result is not necessarily optimal, and would depend on the step; if the marginal utility starts low and grows later, the function won't detect that, it works step by step
• this example works for single number budgets only; here's a bigger example how you could adapt it to dists: https://squigglehub.org/models/quri/optimal-allocation-example (performance is not great though)

It's also possible to implement something more sophisticated in Squiggle.