Sequential decision problems, dependent types and generic solutions

• Published in: Logical methods in computer science 2017, Vol.13 (1)
• Main Authors: Botta, N., Jansson, Patrik, Ionescu, Cesar, Christiansen, D. R., Brady, E.
• Format: Article
• Language: English
• Subjects: Computer and Information Science; Computer Science; computer science - logic in computer science; Data- och informationsvetenskap; Science & Technology - Other Topics
• ISSN: 1860-5974; 1860-5974
• DOI: 10.23638/LMCS-13(1:7)2017

We present a computer-checked generic implementation for solving finite horizon sequential decision problems. This is a wide class of problems, including inter temporal optimizations, knapsack, optimal bracketing, scheduling, etc. The implementation can handle time-step dependent control and state spaces, and monadic representations of uncertainty (such as stochastic, non-deterministic, fuzzy, or combinations thereof). This level of genericity is achievable in a programming language with dependent types (we have used both Idris and Agda). Dependent types are also the means that allow us to obtain a formalization and computer-checked proof of the central component of our implementation: Bellman's principle of optimality and the associated backwards induction algorithm. The formalization clarifies certain aspects of backwards induction and, by making explicit notions such as viability and reachability, can serve as a starting point for a theory of controllability of monadic dynamical systems, commonly encountered in, e.g., climate impact research.