For a little more technical details about IB: To me the idea is to have a way to compactly represent and manipulate an entire set of probability distributions. From that perspective: because of how you can easily maximize/minimize linear functions on convex sets (because the extremum will be some extreme point of the convex set), and since the function from probability distributions to expected value of utility is linear, you can easily find the worst case value on the convex set. For example, you can imagine storing in your head the three vertexes of a triangle, and then quickly finding what the worst case distribution from any part of the triangle would give you.
This lets you efficiently consider more while storing less, which in this view in the whole point.
You can instead take the view that you are ‘totally uncertain’ about which distribution is ‘true’, and so ‘should’ consider convex sets because you can mix any two distributions (e.g. 75% that you draw from distribution X, 25% that you draw from Y).
To me, this line of reasoning is suspect; but it still looks like IB is a good *computational tool*.
For a little more technical details about IB: To me the idea is to have a way to compactly represent and manipulate an entire set of probability distributions. From that perspective: because of how you can easily maximize/minimize linear functions on convex sets (because the extremum will be some extreme point of the convex set), and since the function from probability distributions to expected value of utility is linear, you can easily find the worst case value on the convex set. For example, you can imagine storing in your head the three vertexes of a triangle, and then quickly finding what the worst case distribution from any part of the triangle would give you.
This lets you efficiently consider more while storing less, which in this view in the whole point.
You can instead take the view that you are ‘totally uncertain’ about which distribution is ‘true’, and so ‘should’ consider convex sets because you can mix any two distributions (e.g. 75% that you draw from distribution X, 25% that you draw from Y).
To me, this line of reasoning is suspect; but it still looks like IB is a good *computational tool*.