We have proposed a new approach to decision-making with Quasi-Bayesian models. Quasi-Bayesian theory maintains that a convex set of probability distributions captures the beliefs of an agent. The theory does not specify how two decisions are to be compared when they are both admissible. This has led to a great deal of anxiety among researchers, who have proposed additional constraints to allow any comparison to be made. We depart in a somewhat radical way from this tradition: instead we propose that any admissible decision can be chosen, but that robustness must be monitored by the agent. A non-robust decision must be refined if possible. If there is no time for refinement, a default admissible action is used.
We have demonstrated this approach to decision-making in a problem of planning to observe, where prior beliefs are captured by a set of Gaussian distributions. We demonstrate how to monitor robustness and how to choose E-admissible actions. Our proposal can be extended to the class of planning to observe problems with multivariate data or with general distributions and conjugate priors (for example, beta priors with binomial observations [Lindley and Barnett1965]). Further research is needed to extend these ideas to other, more general decision problems.
The plan generation algorithm here developed is, to the best of our knowledge, the first example of a situation where Quasi-Bayesian theory helps to reduce the complexity of generating a decision plan. This is due to our focus on the robustness, rather than the optimality, of a solution. We expect this approach to shed light on the relationship between rationality requirements and computational effort. Note that we do not suggest that models should be imprecise to facilitate search. We do suggest that the use of a model should be compatible with its precision. The Bayesian strategy sometimes seems excessive in that it forces a precise model into a problem and then demands optimality or meta-analysis with respect to that model. A Quasi-Bayesian approach that focuses on robustness and computational effort can offer a new perspective for decision making.
The theory developed above admits a different, possibly fruitful, interpretation. Suppose an agent has a Quasi-Bayesian model and the agent is not interested in the robustness of actions; instead, the agent wishes to generate admissible actions as fast as possible. This interpretation of Quasi-Bayesian decision making (as advocated by [Good1983]) is that the agent has exhausted preferences and can pick admissible actions arbitrarily. We demonstrated that, for the planning to observe problem, the agent can generate E-admissible plans faster than a Quasi-Bayesian agent could generate a ``best'' plan.
Sun Jul 14 18:32:36 EDT 1996