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Sequential decision problems, dependent types and generic solutions

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Botta_LMCS_13_1_Sequential_CC.pdf (358.2Kb)
Date
17/03/2017
Author
Botta, Nicola
Jansson, Patrik
Ionescu, Cezar
Christiansen, David
Brady, Edwin Charles
Keywords
BC Logic
QA75 Electronic computers. Computer science
T-NDAS
BDC
R2C
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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.
Citation
Botta , N , Jansson , P , Ionescu , C , Christiansen , D & Brady , E C 2017 , ' Sequential decision problems, dependent types and generic solutions ' , Logical Methods in Computer Science , vol. 13 , no. 1 , 7 . https://doi.org/10.23638/LMCS-13(1:7)2017
Publication
Logical Methods in Computer Science
Status
Peer reviewed
DOI
https://doi.org/10.23638/LMCS-13(1:7)2017
ISSN
1860-5974
Type
Journal article
Rights
Copyright the Authors 2017. This work is licensed under the Creative Commons Attribution-NoDerivs License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nd/2.0/
Collections
  • University of St Andrews Research
URL
https://lmcs.episciences.org/3202
URI
http://hdl.handle.net/10023/10681

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