Aligning Learning and Endogenous Decision-Making

TL;DR

This paper presents an end-to-end framework for decision-making under endogenous uncertainty, incorporating robust optimization and a new two-stage stochastic model, with applications in pricing and inventory management showing improved performance.

Contribution

It introduces a novel end-to-end learning approach that accounts for endogenous decision bias, robust optimization over ML models, and a new class of two-stage stochastic problems.

Findings

Robust approach captures near-optimal decisions with high probability.

Framework improves performance over existing online learning and reinforcement learning methods.

New two-stage stochastic model effectively incorporates information gathering before decision-making.

Abstract

Many of the observations we make are biased by our decisions. For instance, the demand of items is impacted by the prices set, and online checkout choices are influenced by the assortments presented. The challenge in decision-making under this setting is the lack of counterfactual information, and the need to learn it instead. We introduce an end-to-end method under endogenous uncertainty to train ML models to be aware of their downstream, enabling their effective use in the decision-making stage. We further introduce a robust optimization variant that accounts for uncertainty in ML models -- specifically by constructing uncertainty sets over the space of ML models and optimizing actions to protect against worst-case predictions. We prove guarantees that this robust approach can capture near-optimal decisions with high probability as a function of data. Besides this, we also introduce a new class of two-stage stochastic optimization problems to the end-to-end learning framework that can now be addressed through our framework. Here, the first stage is an information-gathering problem to decide which random variable to poll and gain information about before making a second-stage decision based off of it. We present several computational experiments for pricing and inventory assortment/recommendation problems. We compare against existing methods in online learning/bandits/offline reinforcement learning and show our approach has consistent improved performance over these. Just as in the endogenous setting, the model's prediction also depends on the first-stage decision made. While this decision does not affect the random variable in this setting, it does affect the correct point forecast that should be made.