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However, current training paradigms suffer from a fundamental limitation: they primarily focus on next-node prediction for solution construction, resulting in myopic decision-making that undermines long-horizon planning capacity. To this end, we introduce Multi-node Lookahead Prediction (MnLP), a novel training strategy that extends the supervised learning paradigm to predict multiple future nodes simultaneously. We incorporate causal and discardable MnLP modules that operate exclusively during training, facilitating models to anticipate multi-step decisions while preserving inference-time efficiency. By incorporating multi-depth auxiliary supervision into the loss function, MnLP equips neural policies with the ability of long-range contextual understanding. Experimentally, MnLP outperforms existing training m","title":"Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Prediction","url":"https://arxiv.org/abs/2605.19975","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.19975v1 Announce Type: cross \nAbstract: Neural policies have shown promise in solving vehicle routing problems due to their reduced reliance on handcrafted heuristics. However, current training paradigms suffer from a fundamental limitation: they primarily focus on next-node prediction for solution construction, resulting in myopic decision-making that undermines long-horizon planning capacity. To this end, we introduce Multi-node Lookahead Prediction (MnLP), a novel training strategy that extends the supervised learning paradigm to predict multiple future nodes simultaneously. We incorporate causal and discardable MnLP modules that operate exclusively during training, facilitating models to anticipate multi-step decisions while preserving inference-time efficiency. By incorporating multi-depth auxiliary supervision into the loss function, MnLP equips neural policies with the ability of long-range contextual understanding. 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