Writing - Overview of a Section

• We resort to reinforcement learning to optimize G 0 in Eq. 2, which can be viewed as a data-driven embodiment of the classic bi-level optimization method by solving two levels of problems alternatively [53]. In Sec. 3.2.1 we present the Markov Decision Process (MDP) formulation of the bi-level optimization in Eq. 2, in Sec. 3.2.2 we describe the PPO learning algorithm in our approach. A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs

• This section explains the Markov decision process (MDP) formulation for the given 2D Euclidean TSP as a representative example. The formulation of MDP for other problems is described in Appendix A.1.Learning Collaborative Policies to Solve NP-hard Routing Problems

• This section describes a novel hierarchical problem-solving strategy, termed learning collaborative policies (LCP), which can effectively find the near-optimum solution using two hierarchical steps, seeding process and revising process (see Figure 1 for detail). In the seeding process, the seeder policy \(p^S\) generates \(M\) number of diversified candidate solutions. In the revising process, the reviser policy \(p^R\) re-writes each candidate solution I times to minimize the tour length of the candidate. The final solution is then selected as the best solution among \(M\) revised (updated) candidate solutions. See pseudo-code in Appendix A.4 for a detailed technical explanation.

• In this part, we describe the details of the proposed Hypergraph Collaborative Network (HCoN), which consists of three main components, i.e., a vertex encoder for learning vertex representations, a hyperedge encoder for learning hyperedge representations, and a decoder for reconstructing the hypergraph. Fig. 2 shows an overview of the proposed model and illustrates how the vertices and hyperedges are collaborative to learn latent representations. After that, we give different objective functions for the vertex and hyperedge classification problems.

  Hypergraph Collaborative Network on Vertices and Hyperedges