Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems

Mathematics. 2024. Vol. 12. No. 21. Article 3321.

Kasianova K., Kelbert M.

 In models with insufficient initial information, there is a possibility of error in their
estimation which can lead to a suboptimal choice being made; however, a delay in implementation
can also lead to losses. This paper examines an extension of information-theoretic approaches
designed to address this classical dilemma, focusing on balancing the expected profits and the
information needed to be obtained about all of the possible outcomes. Initially utilized in binary
outcome scenarios, these methods leverage information measures to harmonize competing objectives
efficiently. Building upon the foundations laid by existing research, this methodology is expanded
to encompass experiments with multiple outcome categories using Dirichlet processes. The core
of our approach is centered around weighted entropy measures, particularly in scenarios dictated
by Dirichlet distributions, which have not been extensively explored previously. We innovatively
adapt the technique initially applied to binary cases to Dirichlet distributions/processes. The primary
contribution of our work is the formulation of a sequential minimization strategy for the main
term of an asymptotic expansion of differential entropy, which scales with sample size, for nonbinary
outcomes. This paper provides a theoretical grounding, extended empirical applications,
and comprehensive proofs, setting a robust framework for further interdisciplinary applications of
information-theoretic paradigms in sequential decision-making.

Keywords: Weighted Information, Information Gain, Bayesian experimental design, Dirichet process

Publication based on the results of: Probabilistic-statistical analysis and modeling of processes with memory, Gaussian chaos, information measures (2024)