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Deep Reinforcement Learning (DRL) is being investigated as a competitive alternative to traditional techniques for solving network optimization problems. A promising research direction lies in enhancing traditional optimization algorithms by offloading low-level decisions to a DRL agent. In this study, we consider how to effectively employ DRL to improve the performance of Local Search algorithms, i.e., algorithms that, starting from a candidate solution, explore the solution space by iteratively applying local changes (i.e., moves), yielding the best solution found in the process. We propose a Local Search algorithm based on lightweight Deep Reinforcement Learning (DeepLS) that, given a neighborhood, queries a DRL agent for choosing a move, with the goal of achieving the best objective value in the long term. Our DRL agent, based on permutation-equivariant neural networks, is composed by less than a …