Decision Making in the Presence of Noise
Michael J. Fischer, Sophia A. Paleologou · Teubner-Texte zur Informatik · 1992
We consider problems of decision making based on imperfect information. We derive Bayesian optimal decision procedures for some simple one-person games on trees in which the player is given redundant but noisy information about the true configuration of the game. Our procedures are computationally efficient, and the decision rules which they implement are describable by simple formulas. Not surprisingly, the presence of noise greatly affects the decision procedure, and decisions procedures that are optimal for the corresponding noiseless games may be far from optimal in the presence of noise. In many cases, the optimal decision depends not only on the given noisy data but also on knowledge of the expected amount of noise present in the data. For arbitrary m ∊ N , we present examples in which the optimal decision changes m times as the probability of error in an individual datum increases from 0 to 1/2. Thus, no decision procedure that is insensitive to (or does not know) the amount of uncertainty in the data can perform as well as one that is aware of the unreliability of its data.