真龍主・星音
二次確率のインントロダクション
Abstract:The first part of this paper presents a basic introduction to second-order
probability theory: what it is, and what kinds of problems it is used to solve.
The remaining parts of this paper introduce a system of theories and
implementations for planning and meta-decision-making with uncertain-outcome
actions represented using second-order probabilities. A situation-based theory of
representing states, situations, and nondeterministic actions is implemented by
the ATMS-based B-SURE system, which supports uncertain-action planning. A
second-order probability theory allows an agent to model a probable continuum of
universes, only one of which is correct; each universe describes a set of possible
worlds labeled with probabilities. This represents the difference between the
likelihood of an outcome and the confidence with which that likelihood is
believed. Confidence is shown to govern meta-decision making, particularly
meta-decisions concerning the gathering of information to clarify outcomes'
likelihoods. Second-order probabilities are defined over partitions and individual
events. Event distributions are convenient but cannot be used for accurate union
nor expectation-distribution conputation. Partition and event distributions are
initialized using maximum-entropy methods which significantly do not require
prior frequency information, and are updated using Bayesian methods. Value of
Information equations are defined, which support meta-decisions. A simple
example demonstrates meta-decision-making with the implemented system. No
other system has used second-order partition probabilities for planning or meta-decision-making.