Max-affine estimators for convex stochastic programming

TL;DR

This paper introduces a new convex regression algorithm using max-affine estimators to approximate convex cost-to-go functions in stochastic programming, demonstrated through energy storage and multi-product assembly problems.

Contribution

The paper presents a novel convex regression method based on max-affine estimators and applies it to approximate dynamic programming in stochastic decision-making problems.

Findings

The max-affine estimator effectively approximates convex functions in stochastic settings.

Empirical evaluation shows improved decision-making performance in energy storage and assembly planning.

The new convex regression algorithm outperforms existing methods in accuracy and efficiency.

Abstract

In this paper, we consider two sequential decision making problems with a convexity structure, namely an energy storage optimization task and a multi-product assembly example. We formulate these problems in the stochastic programming framework and discuss an approximate dynamic programming technique for their solutions. As the cost-to-go functions are convex in these cases, we use max-affine estimates for their approximations. To train such a max-affine estimate, we provide a new convex regression algorithm, and evaluate it empirically for these planning scenarios.