An Alternative to "Maximize Expected Payoff"

Keywords: expected payoff, confidence regions

Abstract: This paper describes an alternative to the popular "take the action which maximizes expected payoff (or minimizes expected cost)" criterion. The alternative is: "take the action which maximizes confidence that a target will be hit (or exceeded)". This alternative has several advantages. First, it may be applied in situations in which the performance of each of several variables is to be controlled. For example, a biomedical researcher may wish to find treatment levels which appropriately control BOTH the T-cell suppressor level (TSL) AND cytotomic cell count (CCC) of AIDS patients. The treatment levels which maximize expected TSL are almost surely not those which maximize CCC, so that the "maximize expected payoff" approach is inappropriate here. However the alternative presented in the paper can be used to find treat- ment levels which maximize confidence that BOTH a TSL target and a CCC target will be hit. Second, the alternative allows the user to produce a "menu" of risk-versus-return trade-offs, by applying it to a sequence of targets (i.e., a sequence of potential returns), and noting the corresponding levels of risk (i,e., confidence that target will be missed). In this paper, the alternative is described in detail, its asymptotic properties are discussed, and the results of a Monte Carlo simulation are presented.