A Dataless Reinforcement Learning Approach to Rounding Hyperplane Optimization for Max-Cut

TL;DR

This paper introduces a dataless reinforcement learning method to improve hyperplane rounding in Max-Cut approximation, outperforming traditional algorithms without requiring training data.

Contribution

It presents a novel non-episodic RL approach that learns to select hyperplanes for Max-Cut, enhancing solution quality over the Goemans-Williamson algorithm.

Findings

Achieves better cuts than GW algorithm on large graphs

Works across graphs with different densities and degrees

Does not require training data or prior domain knowledge

Abstract

The Maximum Cut (MaxCut) problem is NP-Complete, and obtaining its optimal solution is NP-hard in the worst case. As a result, heuristic-based algorithms are commonly used, though their design often requires significant domain expertise. More recently, learning-based methods trained on large (un)labeled datasets have been proposed; however, these approaches often struggle with generalizability and scalability. A well-known approximation algorithm for MaxCut is the Goemans-Williamson (GW) algorithm, which relaxes the Quadratic Unconstrained Binary Optimization (QUBO) formulation into a semidefinite program (SDP). The GW algorithm then applies hyperplane rounding by uniformly sampling a random hyperplane to convert the SDP solution into binary node assignments. In this paper, we propose a training-data-free approach based on a non-episodic reinforcement learning formulation, in which an agent learns to select improved rounding hyperplanes that yield better cuts than those produced by the GW algorithm. By optimizing over a Markov Decision Process (MDP), our method consistently achieves better cuts across large-scale graphs with varying densities and degree distributions.