Sequential Stochastic Combinatorial Optimization Using Hierarchal Reinforcement Learning

TL;DR

This paper introduces a hierarchical reinforcement learning framework called WS-option for sequential stochastic combinatorial optimization, effectively learning adaptive budget allocation and node selection, outperforming traditional methods in efficiency and generalizability.

Contribution

The paper proposes a novel two-layer HRL framework for SSCO, capturing interdependencies and improving efficiency, stability, and scalability over existing approaches.

Findings

WS-option outperforms traditional methods in effectiveness.

The model generalizes well to larger graphs.

It reduces computational overhead significantly.

Abstract

Reinforcement learning (RL) has emerged as a promising tool for combinatorial optimization (CO) problems due to its ability to learn fast, effective, and generalizable solutions. Nonetheless, existing works mostly focus on one-shot deterministic CO, while sequential stochastic CO (SSCO) has rarely been studied despite its broad applications such as adaptive influence maximization (IM) and infectious disease intervention. In this paper, we study the SSCO problem where we first decide the budget (e.g., number of seed nodes in adaptive IM) allocation for all time steps, and then select a set of nodes for each time step. The few existing studies on SSCO simplify the problems by assuming a uniformly distributed budget allocation over the time horizon, yielding suboptimal solutions. We propose a generic hierarchical RL (HRL) framework called wake-sleep option (WS-option), a two-layer option-based framework that simultaneously decides adaptive budget allocation on the higher layer and node selection on the lower layer. WS-option starts with a coherent formulation of the two-layer Markov decision processes (MDPs), capturing the interdependencies between the two layers of decisions. Building on this, WS-option employs several innovative designs to balance the model's training stability and computational efficiency, preventing the vicious cyclic interference issue between the two layers. Empirical results show that WS-option exhibits significantly improved effectiveness and generalizability compared to traditional methods. Moreover, the learned model can be generalized to larger graphs, which significantly reduces the overhead of computational resources.