Deep Reinforcement Learning for Minimum Zero-Forcing Sets

A new reinforcement learning framework called SD-ZFS has been proposed to tackle the NP-hard problem of finding minimum zero-forcing sets on undirected graphs, a challenge with applications in network control and logical circuit design [1]. The minimum zero-forcing set problem is a graph coloring problem in which an initial set of colored nodes propagates its color through a network according to a specific color-change rule, eventually forcing all uncolored nodes to adopt the color [1]. The problem is computationally difficult; finding the minimum zero-forcing set has been proven to be NP-hard [1]. Its practical relevance spans network science, network control, and the design of logical circuits [1]. The SD-ZFS framework adapts the S2V-DQN architecture to the zero-forcing set problem [1]. S2V-DQN is a deep reinforcement learning approach that combines graph embeddings with Q-learning, and the adaptation tailors this mechanism to select nodes that can efficiently force an entire graph. The researchers trained multiple models on the framework and tested them across graph datasets with varying structures [1]. Evaluations measured how well the models generalized to unseen graphs, scaled to larger networks, and transferred across different network types [1]. The results showed that SD-ZFS outperformed a greedy heuristic and approached the performance of the optimal solution on the tested benchmarks [1]. The study also examined how network structure influences the difficulty of the zero-forcing problem, offering insight into which graph characteristics make a set of nodes more or less effective at forcing the entire network [1]. Reinforcement learning frameworks that operate on graphs often rely on neural network components designed for sequential decision-making. Recurrent neural networks, for instance, maintain a hidden state that is updated at each time step based on the current input and the previous hidden state, enabling them to capture temporal dependencies in sequences [5]. While transformer architectures have become dominant for many sequence-processing tasks due to their superior handling of long-range dependencies, recurrent structures remain relevant where computational efficiency or inherent sequential processing is crucial [5]. The SD-ZFS framework's adaptation of S2V-DQN builds on these principles to handle the sequential node-selection process inherent to constructing a zero-forcing set. The work contributes to a broader effort to apply machine learning to combinatorial optimization problems that are intractable for classical algorithms. By demonstrating that a learned heuristic can compete with and sometimes match exact solvers on NP-hard graph problems, the research adds to a growing body of evidence that reinforcement learning can serve as a practical tool for network analysis and design [1].