Towards Effective Planning Strategies for Dynamic Opinion Networks

The spread of information across social networks profoundly impacts public opinion, collective behaviors, and societal outcomes [1]. Especially during crises such as disease outbreaks or disasters, there is often too much information coming from different sources. Sometimes, the resultant flood of information is unreliable or misleading, or spreads too quickly, which can have serious effects on society and health [8]. Online platforms such as Facebook, X, and WeChat, while essential for communication, significantly contribute to the rapid spread of misinformation [2]. This has led to public confusion and panic in events ranging from the Fukushima disaster to the COVID-19 pandemic, and even the U.S. presidential elections [11], demonstrating the need for effective information management on these platforms [8].

The first step in combating misinformation propagation is to reliably detect them. However, detection alone is insufficient to effectively mitigate its spread. It must be complemented with strategic intervention planning to contain its impact. In this context, numerous studies have focused on rumor detection [53, 47, 40, 19], while comprehensive strategies for controlling misinformation are limited [15]. Existing research works on controlling misinformation emphasizes three primary strategies: node removal [9, 45, 29], edge removal [21, 19, 44], and counter-rumor dissemination [5, 42, 12]. Node removal involves identifying and neutralizing key nodes using community detection methods, with dynamic models that adapt to changes in propagation. For example, [50, 16] present ranking algorithms that are critical for identifying influential nodes within complex networks, which can then be targeted to block, remove, or cascade information, to reduce the overall spread of misinformation. These algorithms rank nodes based on various metrics, determining their importance or influence within the network. The second approach, edge removal, focuses on disrupting misinformation pathways by strategically severing connections between nodes. For example, authors in [38] considered mitigating misinformation by identifying potential purveyors to block their posts. However, taking strong measures like censoring user posts may violate user rights.

The third strategy, counter-rumor dissemination, promotes the spread of factual information, leveraging user participation and ‘positive cascades’ to counteract misinformation [41]. For instance, authors in [13] developed a method that involves learning an intervention model to enhance the spread of true news, thereby reducing the influence of fake news. The effectiveness of such intervention planning methods relies on the ability of intervention models to identify key nodes and disseminate accurate/official information through these nodes to mitigate the influence of misinformation. Following this strategy, in [34], a search problem was formulated and sequential plans using automated planning techniques were generated for the targeted spread of information. Despite several model-based efforts to strengthen this approach (see Appendix A.1 for a review of relevant literature), the existing research often overlooks key features of opinion propagation models, such as their rich network dynamics, asynchronous communication, and the impact of factors like the degree of infected nodes, action budget, and various reward models on the effectiveness of planners.

We address this gap by studying the intervention planning problem using two learning methodologies. In both these methodologies, we investigate three distinct cases of opinion network models, ranging from discrete to continuous representations of opinion and mutual trust. Specifically, in this paper, we propose a novel ranking algorithm integrated with a supervised learning (SL) framework to identify influential nodes using a robust feature set of network nodes and evaluate their performance in all three cases. Additionally, we also develop a reinforcement learning (RL)-based solution to design centralized planners that are suitable for larger networks. Furthermore, we develop comprehensive datasets with a wide range of Watts-Strogatz (or small-world) network topologies, varying degrees of initial infected nodes, action budgets, and reward models, e.g., from those requiring local network information to those utilizing global real-time network states, and analyze both the developed methodologies. Next, we use an example to illustrate the intervention planning problem and highlight our contributions.

Our paper makes several significant contributions to intervention planning, focusing on the integration of more realistic and complex modeling approaches, label generation techniques, and training methodologies: (a) We utilize a continuous opinion scale to model the dynamics of misinformation spread (instead of just binary scale as shown in the example), providing a more realistic representation of opinion changes over time. (b) We develop a ranking algorithm for generating labels in networks with discrete opinions, addressing a significant gap in efficient data preparation for SL algorithms in this domain. (c) We develop an RL methodology and perform comprehensive analysis. This allows for adaptive intervention strategies in response to evolving misinformation spread patterns, a critical improvement over traditional static approaches. (d) Utilizing graph convolutional networks (GCNs) with an enhanced feature set of opinion value, connectivity degree, and proximity to a misinformed node, we improve the training of models for selecting effective intervention strategies. This enhancement ensures scalability and generalizes well across various network structures, demonstrating the robust capabilities of GCNs in complex scenarios. Table 3 highlights our contributions by providing a comparative overview of the key features and innovations in our work to that of previous studies. The code and the datasets developed as part of the analysis presented in this paper can be found in [33].

In this section, we discuss our approach to modeling the opinion network environment, the dynamics of information propagation, and our strategy for containing misinformation.

In this section, we will explain our methodologies, presenting an overview of the network architectures employed, including the GCN and ResNet frameworks. Additional details about the neural network architecture utilized for our experiments can be found in Appendix A.2. We detail our proposed ranking algorithm utilized in the SL process. Additionally, we elaborate on the implementation of the Deep Value Network (DVN) with experience replay for the proposed RL-based planners. Furthermore, we provide an explanation of the various reward functions analyzed in our RL setup.

In this section, we present the details about training data generation and configurations chosen for our SL and RL methodologies. We also explain the test data used for evaluating the trained models.

In this section, we evaluate the models, using the infection rate metric, trained using our ranking-based SL and RL algorithms with various reward functions. We discuss the efficiency of these models using Dataset v2, particularly on a network of 50 nodes with a connectivity degree of 4, as it represents the most complex test dataset we generated. Similar evaluation results for other datasets can be found in the Appendix A.6. Additionally, we have also evaluated our planning algorithms using directed and undirected real-world network models reported in the literature. These evaluations are presented in Table 2. The details of the hardware used for our experiments are provided in the Appendix A.4. Our empirical investigation yielded insightful results regarding the performance of our trained models under various training conditions. With comprehensive experimental evaluations, we were able to address the following research questions.

Objective and Research Questions: O: Identify the optimal combination of initially infected nodes and action budget parameters for training models to effectively control the spread of misinformation. RQ1: For reward functions that focus on the blocking time, does adding any other factor lead to better results? If yes, which factor? RQ2: Do reward functions that look at global graph information perform better than those considering local, neighboring information? RQ3: Does GCN offer better scalability and performance when compared with ResNet.

O: What is the best combination of initially infected nodes and action budget parameters for training the models to control the misinformation spread?

To examine this, we focused our analysis on the Mean Squared Error (MSE) loss plots obtained during the training phase. Figure 7 in Appendix A.6 illustrates the comparison of training loss across various network parameter settings for all considered reward types in Case-1, employing a ResNet model trained on a network of 50 nodes. The trend in loss convergence across episodes was found to be consistent for both the ResNet and GCN models across all cases examined. The analysis revealed that reward functions exhibiting lower and more stable loss values correlate with improved model learning performance. Our findings highlight that increasing the number of initially infected nodes typically elevates the stabilization point of MSE loss, indicating a more challenging learning environment. Additionally, a higher action budget contributes to increased MSE variability, reflecting the added complexity and generally poorer performance during training. Based on this analysis, we find ResNet-$n$-$1$-$1$ and GCN-$n$-$1$-$1$, $n\in$ {10,25,50}, to be the best training configurations.

Table 1 presents the average infection rate values across different cases considered for Dataset v2 with a degree of connectivity 4, featuring a network of 50 nodes, detailing the average infection rates. It compares the performance of the ResNet model, trained on a network of 50 nodes, with the GCN model, trained on a network of 10 nodes, using the RL training algorithm across the different reward types, and the GCN model trained using SL on a network of 25 nodes. Results on the additional datasets are provided in Appendix A.6.

RQ1: For reward functions that focus on blocking time, does adding any other factor lead to better result? If yes, which factor? Answer: Yes. #candidate nodes.

Reward function $R_{3}$, which is formulated to minimize the number of time steps required to halt the spread of misinformation, might inadvertently not be the most effective strategy for minimizing the overall infection rate within the network. As the reward is solely based on the speed of response, it does not directly account for the magnitude of the misinformation spread, that is, the number of nodes affected. Therefore, the agent may prioritize actions that conclude the propagation swiftly but do not necessarily result in the most substantial reduction in the spread of misinformation. However, our results indicate that under specific training configurations with an action budget or initial infected nodes greater than $1$, the reward function $R_{3}$ outperforms others in maintaining lower infection rates, as shown in Figure 8 in Appendix A.6. This finding is significant since $R_{3}$, a sparser reward type, requires less computational effort and is independent of network observability. As the action budget increases the propagation tends to conclude in fewer timesteps thereby resulting in the RL agent receiving a higher reward in the case of $R_{3}$. Figure 2 shows that the RL agent trained with the $R_{3}$ reward function chooses actions that conclude propagation in the least time. Conversely, Figure 1 illustrates the sequence of actions chosen by an RL agent trained with the $R_{1}$ reward function on the same network. Although $R_{1}$ requires more time steps than $R_{3}$, it results in a lower infection rate. This can also be observed from Table 1, where the infection rate is higher for the $R_{3}$ reward function than any other reward function. In order to effectively implement this we have considered combining this episodic reward along with $R_{1}$, resulting in reward type $R_{5}$. This has shown a significant performance improvement when compared to the original version.

RQ2: Do reward functions that look at global graph information perform better than those considering local, neighboring information ? Answer: Yes

Analysis of the inference outcomes using Dataset v2, as presented in Table 1, shows that single factor reward functions, specifically $R_{1}=-(\text{\# candidate nodes})$ and $R_{4}=-(\text{infection rate})$, consistently resulted in lower infection rates across various settings compared to their more complex counterparts with $R_{4}$ providing relatively better results compared to $R_{1}$. This trend was observed in both ResNet and GCN models. From a practical standpoint, $R_{1}$ can be particularly advantageous because it does not require complete observability of the network, but just the immediate neighbors of infected nodes. Conversely, to compute $R_{4}$, which reflects the infection rate of the network, complete understanding of the state of each node within the network is required. This requirement for total network observability could limit the practicality of $R_{4}$ in situations where such detailed information is unavailable or difficult to gather.

RQ3: Does GCN offer better scalability and performance when compared with ResNet? Answer: Yes

GCNs are hypothesized to outperform traditional convolution-based architectures like ResNet in tasks involving graph data due to their ability to naturally process the structural information of networks and their enhanced ability to represent complex feature sets [4]. This study compares the scalability and performance of a GCN, which excels in node classification within graphs, to a ResNet model that, despite its success in image recognition, may not scale as effectively to larger graph structures beyond the size it was initially trained on. Referring to Table 1, the GCN model, trained on only 10 node networks, consistently exhibits lower average infection rates across all the cases and under varying action budgets, when compared with the ResNet model trained on 50 node networks. The ability of GCN to maintain lower infection rates even as network complexity increases underscores its robustness and scalability in more complex network scenarios. This performance contrast highlights the suitability of GCN architectures for graph-based tasks.

This paper investigates scalable and innovative intervention strategies for containing the spread of misinformation within dynamic opinion networks. Our significant contributions include analysis using continuous opinion models, a design of ranking algorithm for identifying key nodes to facilitate SL-based classifiers, and the utilization of GCNs to optimize intervention strategies. Additionally, we design and study various reward functions for reinforcement learning, enhancing our approach to misinformation mitigation.

Despite significant progress, our work has limitations. In the field of computational social science, often more complex agent models are being investigated. While we have made significant efforts to extend the understanding of planning strategies, especially in continuous opinion networks, exploring complex agent traits such as stubbornness and the representation of directed trust, and implementing topic-dependency in a multi-topic network along with distributed planners instead of centralized planners as in our work is a compelling future direction.

Broader Societal Impact: This work provides methods that can be used to exert control on information spread. When used responsibly by authorized information providers, which the authors support, it will help reduce prevalent infodemics in social media. But it may also be misused by an adversary to wean control from an authorized party (e.g., information owner) and counter efforts to tackle misinformation. Overall, the authors believe more research efforts are needed to understand opinion networks and information dissemination strategies in dynamic and uncertain environments in pursuit of long-term societal benefits.

This material is based upon work supported in parts by the Air Force Office of Scientific Research under award number FA9550-24-1-0228 and NSF award number 2337998. Any opinions, findings, conclusions, or recommendations expressed here are those of the authors and do not necessarily reflect the views of the sponsors. The authors thank the anonymous reviewers for their insightful and constructive reviews.