“Guaranteed performance” typically cashes out as “replace the value of an action with the probability that its outcome is better than L, then pick the best” whereas “optimizing for the worst case” typically cashes out as “replace the value of an action with the value of its worst outcome, then pick the best.”
The latter is often referred to as “robustness” and the former as “partial robustness,” and which one is applicable depends on the situation. Generally, the latter is used in problems with severe probabilistic uncertainty, whereas the former needs some probabilistic certainty.
“Guaranteed performance” typically cashes out as “replace the value of an action with the probability that its outcome is better than L, then pick the best” whereas “optimizing for the worst case” typically cashes out as “replace the value of an action with the value of its worst outcome, then pick the best.”
The latter is often referred to as “robustness” and the former as “partial robustness,” and which one is applicable depends on the situation. Generally, the latter is used in problems with severe probabilistic uncertainty, whereas the former needs some probabilistic certainty.