Discounted Pseudocosts in MILP

TL;DR

This paper introduces discounted pseudocosts, inspired by reinforcement learning, to improve branching strategies in MILP, showing promising results in accelerating solutions on benchmark instances.

Contribution

It proposes a novel approach to pseudocost estimation in MILP using discounted rewards, integrating reinforcement learning concepts.

Findings

Enhanced branching strategies with discounted pseudocosts

Improved solution speed on MIPLIB 2017 instances

Potential for better MILP performance with the new method

Abstract

In this article, we introduce the concept of discounted pseudocosts, inspired by discounted total reward in reinforcement learning, and explore their application in mixed-integer linear programming (MILP). Traditional pseudocosts estimate changes in the objective function due to variable bound changes during the branch-and-bound process. By integrating reinforcement learning concepts, we propose a novel approach incorporating a forward-looking perspective into pseudocost estimation. We present the motivation behind discounted pseudocosts and discuss how they represent the anticipated reward for branching after one level of exploration in the MILP problem space. Initial experiments on MIPLIB 2017 benchmark instances demonstrate the potential of discounted pseudocosts to enhance branching strategies and accelerate the solution process for challenging MILP problems.