Pointer Networks with Q-Learning for Combinatorial Optimization

Abstract: We introduce the Pointer Q-Network (PQN), a hybrid neural architecture that integrates model-free Q-value policy approximation with Pointer Networks (Ptr-Nets) to enhance the optimality of attention-based sequence generation, focusing on long-term outcomes. This integration proves particularly effective in solving combinatorial optimization (CO) tasks, especially the Travelling Salesman Problem (TSP), which is the focus of our study. We address this challenge by defining a Markov Decision Process (MDP) compatible with PQN, which involves iterative graph embedding, encoding and decoding by an LSTM-based recurrent neural network. This process generates a context vector and computes raw attention scores, which are dynamically adjusted by Q-values calculated for all available state-action pairs before applying softmax. The resulting attention vector is utilized as an action distribution, with actions selected hinged to exploration-exploitation dynamic adaptibility of PQN. Our empirical results demonstrate the efficacy of this approach, also testing the model in unstable environments.