It appears to be a general principle that, whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought. – E.T.Jaynes.

We learn random and stochastic concepts help us fight against the world full of the unknown. Page rank and Monte Carlo sampling algorithms support the perspective. However, from the quote, Jaynes explains there exists a nonrandom substitute for a random component in general. Should we view randomness as something to be replaced or could there be any example where randomness is the optimal tool we have?

One way to view this is exploration vs exploitation. ‘Random’ may be the global optimal solution (operator to be precise), but it could give way to its nonrandom counterpart once the problem space is restricted to its subspace. Aside from the exploration, designing a nonrandom operator that exploits the targeted homogeneity from restriction is costly. So our role as a researcher could be to find a sizable restriction of a problem space on which nonrandom solution shows performance improvement (ideally uniform, if not on average).

Maybe the research’s cooperative effort of substituting the random to nonrandom are what protect us against entropy ever-increasing world.

– Moon