Collective Wisdom: Policy Averaging with an Application to the Newsvendor Problem

We propose a Policy Averaging Approach (PAA) that synthesizes the strengths of existing approaches to create more reliable, flexible and justifiable policies for stochastic optimization problems. An important component of the PAA is risk diversification to reduce the randomness of policies. A second component emulates model averaging from statistics. A third component involves using cross-validation to diversify and optimize weights among candidate policies. We demonstrate the use of the PAA for the newsvendor problem. For that problem, model-based approaches typically use specific and potentially unreliable assumptions of either independently and identically distributed (i.i.d.) demand or feature-dependent demand with covariates or autoregressive functions. Data-driven approaches, including sample averaging and the use of functions of covariates to set order quantities, typically suffer from overfitting and provide limited insights to justify recommended policies. By integrating concepts from statistics and finance, the PAA avoids these problems. We show using theoretical analysis, a simulation study, and an empirical study, that the PAA outperforms all those earlier approaches. The demonstrated benefits of the PAA include reduced expected cost, more stable performance, and improved insights to justify recommendations. Extensions to consider tail risk and the use of stratified sampling are discussed. Beyond the newsvendor problem, the PAA is applicable to a wide variety of decision-making problems under uncertainty.