Summary
We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm using pure exploitation, where the states we visit depend on the decisions produced by solving the approximate problem. The resulting algorithm does not require knowing the probability distribution of prices or demands, nor does it require any assumptions about its functional form. The algorithm and its proof rely on the fact that the true value function is a family of piecewise linear concave functions.
Outcomes reported
Referenced by Nature Communications British biodiversity scenarios as citation 164; likely supports topic area: biodiversity / conservation. Topics: biodiversity / conservation Evidence type: Report Source report: Nature Communications British biodiversity scenarios Ref#: Nature Communications British biodiversity scenarios #164 Original: Powell, M. J. D. The BOBYQA algorithm for bound constrained optimization without derivatives. Technical Report DAMTP 2009/ NA06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge (2009).
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