The "algorithm" is descriptive, it's really a definition of optimality of a decision, not specification of how this decision is to be computed. You can sometimes optimize infinities away, and can almost always find a finite approximation that gets better with more resources and ingenuity.

Okay. I didn't know that the specification of how to compute was explicitly understood to be incomplete in this way. Of course, the description could only be improved by being more specific about just when you can "sometimes optimize infinities away, and can almost always find a finite approximation that gets better with more resources and ingenuity."