Summary

We propose a scalable deep learning framework for parametrized sequential decision-making (ParaSDM), where multiple agents jointly optimize discrete action policies and shared continuous parameters. A key subclass of this setting arises in Facility-Location and Path Optimization (FLPO), where multi-agent systems must simultaneously determine optimal routes and facility locations, aiming to minimize the cumulative transportation cost within the network. FLPO problems are NP-hard due to their mixed discrete-continuous structure and highly non-convex objective. To address this, we integrate the Maximum Entropy Principle (MEP) with a neural policy model called the Shortest Path Network (SPN)-a permutation-invariant encoder-decoder that approximates the MEP solution while enabling efficient gradient-based optimization over shared parameters. The SPN achieves up to 100× speedup in policy inference and gradient computation compared to MEP baselines, with an average optimality gap of approximately 6% across a wide range of problem sizes. Our FLPO approach yields over 10× lower cost than metaheuristic baselines while running significantly faster, and matches Gurobi's optimal cost with annealing at a 1500× speedup-establishing a new state of the art for ParaSDM problems. These results highlight the power of structured deep models for solving large-scale mixed-integer optimization tasks.