A New Optimal Stepsize For Approximate Dynamic Programming

TL;DR

This paper introduces a new stepsize rule for approximate dynamic programming that enhances convergence speed and robustness by optimizing prediction error with minimal tuning.

Contribution

A novel stepsize rule for ADP that automatically adapts to noise levels, improving short-term performance and convergence without extensive parameter tuning.

Findings

Faster convergence in numerical experiments

Robust performance across different noise levels

Minimal parameter tuning required

Abstract

Approximate dynamic programming (ADP) has proven itself in a wide range of applications spanning large-scale transportation problems, health care, revenue management, and energy systems. The design of effective ADP algorithms has many dimensions, but one crucial factor is the stepsize rule used to update a value function approximation. Many operations research applications are computationally intensive, and it is important to obtain good results quickly. Furthermore, the most popular stepsize formulas use tunable parameters and can produce very poor results if tuned improperly. We derive a new stepsize rule that optimizes the prediction error in order to improve the short-term performance of an ADP algorithm. With only one, relatively insensitive tunable parameter, the new rule adapts to the level of noise in the problem and produces faster convergence in numerical experiments.