Incremental Constraint-Based Elicitation of Multi-Attribute Utility Functions

摘要

In problem solving, the decision-theoretic framework is invoked when we wish to define a rich notion of preference over possible solutions. While decision theory provides a clean framwork for representing preference information, eliciting that information can often be difficult. When solutions are simply concrete outcomes, preferences can be represented directly by simply ranking the outcomes. But when solutions can have uncertain outcomes, this is not feasible and preferences are typically represented with a real-valued utility function over outcomes, which captures a decision-maker's attitudes toward risk. Even in the case of complete certainty, preferences are often represented by a real-valued function over outcomes, called a value function. Outcome space is typically defined in terms of a set of attributes, with an outcome being a complete assignment of values to all the attributes. For realistic decision-making problems the outcome space if usually too large to allow direct specification of utility and value functions, so assumptions are made that allow them to be specified in terms of component functions for each of the attributes. The assumptions concern independence of a user's preferences over values of one or more attributes as the values of other attributes are varied. Most work on elicitation has made the strong assumption of additive independence among the attributes. In this work we make the weaker assumption of simple utility independence among the attributes, which gives rise to a multi-linear form of utility function. Such a function is too complex to elicit directly, so instead we show how we can indirectly infer constraints on the utility function by eliciting pairwise preferences among solutions from the decision maker. We assume that the set of solutions is finite and that the decision maker is comfortable expressing pairwise preferences among some fraction of the solutions. For some problems it can be easier for a decision maker to express preference among solution alternatives than to introspect about the attributes describing each one. For example, in expressing preferences about movies most people can almost instantly express their preference among two films they have seen but may have difficulty describing preferences over attributes like director, leading actor, costume designer, etc. In fact, most people would not even recognize the names of costume designers.