K-Spin Ising Model for Combinatorial Optimizations over Graphs: A Reinforcement Learning Approach
Keywords: K-Spin Ising Model, Combinatorial Optimizations over Graphs, reinforcement learning
Abstract: Many graph-based combinatorial optimization (GCO) problems are NP-complete and can be formulated by the Ising model. Reinforcement learning (RL) algorithms are promising due to their powerful search abilities. The sampling method in RL is the Monte Carlo Markov chain (MCMC), which collects many samples on a trajectory, while we can only obtain one objective value for a GCO problem if using the Ising model. In this paper, we propose a K-spin Ising model for GCO problems, which integrates well with RL algorithms. First, we propose a \textit{K-spin Ising model} and use its Hamiltonian as the loss function, which collects samples on trajectories. Second, we give the K-spin Hamiltonian functions for several GCO problems. Third, we evaluate our RL approach for the graph maxcut problem on both synthetic and benchmark datasets. Our approach outperforms the commercial solver Gurobi \cite{2023gurobi} with a speedup of $100 \times$ and $10 \times$ in small-scale ($100 \sim 3,000$ nodes) and large-scale ($5,000 \sim 10,000$ nodes) graph instances, respectively. On the benchmark dataset, our approach obtains nearly the same best-known results over five compared methods.
Submission Number: 2
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