In The Real Rules have No Exceptions, Said says (apparently speaking of instrumental rules, not epistemic ones):
Prefer simplicity in your rules. Be vigilant that your rules do not grow too complex; make sure you are not relaxing the legitimacy criteria of your exceptions. Periodically audit your rules, inspecting them for complexity; try to formulate simpler versions of complex rules.
This is a very plausible principle. I have had similar thoughts myself. The idea seems to have merit in practice. But is there any theoretical analogue?
Minimum description length (Occam's Razor) is an epistemic principle. In Bayesian terms, probabilities must sum to one, which translates information-theoretically (via optimal encodings) to the idea that there are only so many short codes, so we have to assign them carefully to the most probable things.
However, expected utility is not a limited resource in this way. Updating to think an option is better than previously thought doesn't necessarily make other options worse. Selecting policies is not so different from selecting raw actions. And for Bayesian decision theory, it doesn't really matter whether a policy is specified as a big table of observation/action pairs, vs an elegantly specified rule.
Optimality cares not for elegance!
Yet, even in the relatively formal world of machine learning, the practice seems contrary to this. When you are optimizing a neural network, you don't actually care that much whether it's something like a hypothesis (making predictions) or something like a policy (carrying out actions). You apply the same kind of regularization either way, as far as I understand (regularization being the machine-learner's generalization of Occam). (Correction: this seems not to be the case.)
We might say that this is because (in some sense) the instrumental uncertainty and the epistemic uncertainty are actually being wrapped up together. But (1) this reply seems overly quick to me at present, and I'd want to understand in detail whether this can be justified; (2) I'm curious if there is a purely instrumental version of Occam to be articulated; it seems intuitively really plausible to me, though technically quite mysterious.
So: is it possible to formulate an instrumental version of Occam? Can we justify a simplicity bias in our policies?