Sequential decision problems, dependent types and generic solutions

Nicola Botta, Patrik Jansson, Cezar Ionescu, David Christiansen, Edwin Charles Brady

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We present a computer-checked generic implementation for solving finite horizon sequential decision problems. This is a wide class of problems, including intertemporal 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.
Original languageEnglish
Article number7
Number of pages23
JournalLogical Methods in Computer Science
Volume13
Issue number1
DOIs
Publication statusPublished - 17 Mar 2017

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