I like this point of view.

ETA: A couple commenters are saying it is bad or discouraging that you can't optimize over non-compact sets, or that this exposes a flaw in ordinary decision theory. My response is that life is like an infinitely tall drinking-glass, and you can put as much water as you like in it. You could look at the glass and say, "it will always be mostly empty", or you could look at it and say "the glass can hold an awful lot of water".