Sequential decision problems, dependent types and generic solutions
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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.
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
Logical Methods in Computer Science
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