Model Ensembling for Constrained Optimization

TL;DR

This paper develops algorithms for ensembling models with multidimensional outputs to optimize downstream objectives under constraints, using multicalibration techniques with proven efficiency and convergence guarantees.

Contribution

It introduces two novel algorithms, white box and black box, for ensembling models in constrained optimization, with theoretical guarantees and experimental evaluation.

Findings

Both algorithms outperform individual models in optimization tasks.

The white box approach requires models; the black box only needs policies.

Algorithms are proven to be efficient and convergent.

Abstract

There is a long history in machine learning of model ensembling, beginning with boosting and bagging and continuing to the present day. Much of this history has focused on combining models for classification and regression, but recently there is interest in more complex settings such as ensembling policies in reinforcement learning. Strong connections have also emerged between ensembling and multicalibration techniques. In this work, we further investigate these themes by considering a setting in which we wish to ensemble models for multidimensional output predictions that are in turn used for downstream optimization. More precisely, we imagine we are given a number of models mapping a state space to multidimensional real-valued predictions. These predictions form the coefficients of a linear objective that we would like to optimize under specified constraints. The fundamental question we address is how to improve and combine such models in a way that outperforms the best of them in the downstream optimization problem. We apply multicalibration techniques that lead to two provably efficient and convergent algorithms. The first of these (the white box approach) requires being given models that map states to output predictions, while the second (the \emph{black box} approach) requires only policies (mappings from states to solutions to the optimization problem). For both, we provide convergence and utility guarantees. We conclude by investigating the performance and behavior of the two algorithms in a controlled experimental setting.