Title: LPMARL: Linear Programming based Implicit Task Assignment for Hierarchical Multi-agent Reinforcement Learning. Abstract: Training a multi-agent reinforcement learning (MARL) model with sparse reward is notoriously difficult because the terminal reward is induced by numerous interactions among agents. In this study, we propose linear programming-based hierarchical MARL (LPMARL) to learn effective coperative strategy among agents. LPMARL is composed of two hierarchical decision-making schemes: (1) solving an agent-task assignment problem and (2) solving a local cooperative game among agents that are assigned to the same task. For the first step, LPMARL formulates the agent-task assignment problem as linear programming (LP) using the state-dependent cost parameters generated by a graph neural network (GNN). Solving the LP can be considered as assigning tasks to agents, which decomposes the original problem into a set of task-dependent sub-problems. After solving the formulated LP, LPMARL employs a general MARL strategy to derive a lower-level policy to solve each sub-task in a cooperative manner. We train the LP-parameter generating GNN layer and the low-level MARL policy network, which are the essential components for making hierarchical decisions, in an end-to-end manner using the implicit function theorem. We empirically demonstrate that LPMARL learns an optimal agent-task allocation and the subsequent local cooperative control policy among agents in sub-groups for solving various mixed cooperative-competitive environments.