There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused onobtaining high-quality solutions, scalability tobillion-sized graphs has not been adequately addressed.

There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of a budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node. To further facilitate the combinatorial nature of the problem, GCOMB utilizes a Q-learning framework, which is made efficient through importance sampling. We perform extensive experiments on real graphs to benchmark the efficiency and efficacy of GCOMB. Our results establish that GCOMB is 100 times faster and marginally better in quality than state-of-the-art algorithms for learning combinatorial algorithms. Additionally, a case-study on the practical combinatorial problem of Influence Maximization (IM) shows GCOMB is 150 times faster than the specialized IM algorithm IMM with similar quality.

Weaknesses: The main weaknesses of the paper are that the work only uses a naïve version of the greedy algorithm rather than the faster lazy greedy algorithm, and that it seems to claim more than the results suggest without further investigation in terms of the scope of applicability, and performance improvements over the greedy algorithm. The approach seems to be specialized to selecting a set of elements for coverage-like problems and specifically submodular maximization problems which admit greedy approximation algorithms, not necessarily general set combinatorial problems as claimed (it is important to clearly and fairly articulate the claimed scope of the proposed algorithms superior performance). Additionally, the greedy algorithm empirically gives near-optimal performance in the experiments, so it would be useful to know whether this approach performs well for more difficult problems, where greedy is not almost optimal. It would be good to see performance on other more combinatorial problems or nonsubmodular set graph problems, e.g. The score supervision used to train the GCN is highly related to the marginal return that greedy would use to score nodes. In addition, the locality metric seems to directly consider the percent of neighbors of a node which are not currently covered by a partial solution, which is directly related to the coverage problems considered in this work.

Three reviewers rated this paper as weak accept, and one as reject. All reviewers felt the paper combined learning-based techniques effectively to achieve impressive performance on combinatorial optimization problems in massive graphs. Reviewers describe the work as a combination of heuristics and modules consisting of existing techniques, but largely view the overall system as being significant, and comment on its impressive performance and an ablation study to justify individual components. The main criticisms were about missing comparisons to baselines. It was observed that the proposed method essentially does well on submodular coverage style problems where the greedy algorithm is often nearly optimal in practice and its main advantage is being much faster.

There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of a budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node.

Recent years have witnessed a growing trend toward employing deep reinforcement learning (Deep-RL) to derive heuristics for combinatorial optimization (CO) problems on graphs. Maximum Coverage Problem (MCP) and its probabilistic variant on social networks, Influence Maximization (IM), have been particularly prominent in this line of research. In this paper, we present a comprehensive benchmark study that thoroughly investigates the effectiveness and efficiency of five recent Deep-RL methods for MCP and IM. These methods were published in top data science venues, namely S2V-DQN, Geometric-QN, GCOMB, RL4IM, and LeNSE. Our findings reveal that, across various scenarios, the Lazy Greedy algorithm consistently outperforms all Deep-RL methods for MCP. In the case of IM, theoretically sound algorithms like IMM and OPIM demonstrate superior performance compared to Deep-RL methods in most scenarios. Notably, we observe an abnormal phenomenon in IM problem where Deep-RL methods slightly outperform IMM and OPIM when the influence spread nearly does not increase as the budget increases. Furthermore, our experimental results highlight common issues when applying Deep-RL methods to MCP and IM in practical settings. Finally, we discuss potential avenues for improving Deep-RL methods. Our benchmark study sheds light on potential challenges in current deep reinforcement learning research for solving combinatorial optimization problems.

Aiming at selecting a small subset of nodes with maximum influence on networks, the Influence Maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-the-art methods, including heuristic and approximation algorithms, faced with great difficulties such as theoretical guarantee, time efficiency, generalization, etc. This makes it unable to adapt to large-scale networks and more complex applications. On the other side, with the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, lots of works have been focused on exploiting DRL to solve combinatorial optimization problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this paper, which incorporates three coupled graph neural networks for network embedding and double deep Q-networks for parameters learning. Previous efforts to solve IM problem with DRL trained their models on subgraphs of the whole network, and then tested on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs with a small budget, and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets, and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets, and experimental results prove the effectiveness and superiority of our model.

In this paper, we propose a deep reinforcement learning framework called GCOMB to learn algorithms that can solve combinatorial problems over large graphs. GCOMB mimics the greedy algorithm in the original problem and incrementally constructs a solution. The proposed framework utilizes Graph Convolutional Network (GCN) to generate node embeddings that predicts the potential nodes in the solution set from the entire node set. These embeddings enable an efficient training process to learn the greedy policy via Q-learning. Through extensive evaluation on several real and synthetic datasets containing up to a million nodes, we establish that GCOMB is up to 41% better than the state of the art, up to seven times faster than the greedy algorithm, robust and scalable to large dynamic networks.