Why is Resorting to Fate Wise? A Critical Look at Randomized Algorithms in Systems and Control

During recent years, the systems and control community has experienced a growing interest in randomized algorithms, and there appears to be a wide-spread excitement for methods incorporating randomized features since these methods seem to be capable of transcending some traditional difficulties inherent in deterministic approaches, especially in relation to computational issues. Upon reflection, a randomized algorithm is nothing but a procedure where one or more steps are based on a random rule, that is, when using a randomized algorithm, at some stage instead of making a decision ourselves we call on fate to choose for us. But then, a question arises naturally: why should resorting to fate be any wise? Fate is not an expert of anything, all it does is choosing by chance. So, why should randomized be any good? A conscious use of randomized methods demands to question ourselves about this issue, and this write-up contains my reflections on this matter.