Design of reward structures for sequential decision-making processes using symbolic analysis

In this paper we construct a symbolic mathematical model for a deterministic decision-making process, called the win-stay lose-switch model, that has been used recently to study human behaviors in a class of two-alternative, sequential, decision-making tasks. The human decisions in these tasks are conditioned by the provision of certain rewards after each taken decision. Our modeling approach allows us to use symbolic analysis techniques to verify or design reward structures guaranteeing that the process of decision making respects pre-specified temporal properties. More importantly, it enables the study of properties going beyond the asymptotic behavior of the decision process. The proposed approach could prove useful to facilitate the interaction of a human user learning to interact with smart machines.