Stochastic Optimization Forests

Nathan Kallus () and Xiaojie Mao ()
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Nathan Kallus: Cornell Tech, Cornell University, New York, New York 10044
Xiaojie Mao: School of Economics and Management, Tsinghua University, Beijing 100084, China

Management Science, 2023, vol. 69, issue 4, 1975-1994

Abstract: We study contextual stochastic optimization problems, where we leverage rich auxiliary observations (e.g., product characteristics) to improve decision making with uncertain variables (e.g., demand). We show how to train forest decision policies for this problem by growing trees that choose splits to directly optimize the downstream decision quality rather than split to improve prediction accuracy as in the standard random forest algorithm. We realize this seemingly computationally intractable problem by developing approximate splitting criteria that use optimization perturbation analysis to eschew burdensome reoptimization for every candidate split, so that our method scales to large-scale problems. We prove that our splitting criteria consistently approximate the true risk and that our method achieves asymptotic optimality. We extensively validate our method empirically, demonstrating the value of optimization-aware construction of forests and the success of our efficient approximations. We show that our approximate splitting criteria can reduce running time hundredfold while achieving performance close to forest algorithms that exactly reoptimize for every candidate split.

Keywords: contextual stochastic optimization; decision making under uncertainty with side observations; random forests; perturbation analysis (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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