Learning What to Defer for Maximum Independent Sets

TL;DR

This paper introduces a novel deep reinforcement learning framework called learning what to defer (LwD) for solving maximum independent set problems more efficiently, especially on large-scale graphs, by adaptively adjusting decision stages.

Contribution

The paper proposes the LwD scheme that adaptively adjusts decision stages in DRL for MIS, enabling better scalability and performance on large graphs.

Findings

LwD significantly outperforms existing DRL schemes in MIS tasks.

LwD achieves superior results on large graphs with millions of vertices.

LwD outperforms traditional MIS solvers within limited time budgets.

Abstract

Designing efficient algorithms for combinatorial optimization appears ubiquitously in various scientific fields. Recently, deep reinforcement learning (DRL) frameworks have gained considerable attention as a new approach: they can automate the design of a solver while relying less on sophisticated domain knowledge of the target problem. However, the existing DRL solvers determine the solution using a number of stages proportional to the number of elements in the solution, which severely limits their applicability to large-scale graphs. In this paper, we seek to resolve this issue by proposing a novel DRL scheme, coined learning what to defer (LwD), where the agent adaptively shrinks or stretch the number of stages by learning to distribute the element-wise decisions of the solution at each stage. We apply the proposed framework to the maximum independent set (MIS) problem, and demonstrate its significant improvement over the current state-of-the-art DRL scheme. We also show that LwD can outperform the conventional MIS solvers on large-scale graphs having millions of vertices, under a limited time budget.