It's not clear or obvious why continuous semantics should be applicable on a digital computer. This might seem like nitpicking but it's not, there is a fundamental issue that is always swept under the rug in these kinds of analysis which is about reconciling finitary arithmetic over bit strings & the analytical equations which only work w/ infinite precision over the real or complex numbers as they are usually defined (equivalence classes of cauchy sequences or dedekind cuts).

There are no dedekind cuts or cauchy sequences on digital computers so the fact that the analytical equations map to algorithms at all is very non-obvious.

One interesting connection is that many production AI systems don't explicitly implement RL frameworks, but still behave like RL systems.

You still have: state -> user context action -> model output reward -> engagement or success metric

Once that loop exists, optimization dynamics start to look very similar.

Ever since the control bug bit me in my EE undergrad years I am happy to see how useful the knowledge remains. Of course the underlying math of optimization remains general but the direct applications of control theory made it much more appetizing for me to struggle through.