What AlexMennen said. For a Bayesian there's no difference in principle between ignorance and risk.

One wrinkle is that even Bayesians shouldn't have prior probabilities for everything, because if you assign a prior probability to something that could indirectly depend on your decision, you might lose out.

A good example is the absent-minded driver problem. While driving home from work, you pass two identical-looking intersections. At the first one you're supposed to go straight, at the second one you're supposed to turn. If you do everything correctly, you get utility 4. If you goof and turn at the first intersection, you never arrive at the second one, and get utility 0. If you goof and go straight at the second, you get utility 1. Unfortunately, by the time you get to the second one, you forget whether you'd already been at the first, which means at both intersections you're uncertain about your location.

If you treat your uncertainty about location as a probability and choose the Bayesian-optimal action, you'll get demonstrably worse results than if you'd planned your actions in advance or used UDT. The reason, as pointed out by taw and pengvado, is that your probability of arriving at the second intersection depends on your decision to go straight or turn at the first one, so treating it as unchangeable leads to weird errors.