Botta, Nicola and Jansson, Patrik and Ionescu, Cezar and Christiansen, David R. and Brady, Edwin - Sequential decision problems, dependent types and generic solutions

lmcs:3202 - Logical Methods in Computer Science, March 17, 2017, Volume 13, Issue 1
Sequential decision problems, dependent types and generic solutions

Authors: Botta, Nicola and Jansson, Patrik and Ionescu, Cezar and Christiansen, David R. and Brady, Edwin

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.


Source : oai:arXiv.org:1610.07145
DOI : 10.23638/LMCS-13(1:7)2017
Volume: Volume 13, Issue 1
Published on: March 17, 2017
Submitted on: March 17, 2017
Keywords: Computer Science - Logic in Computer Science


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