In cooperative multi-agent reinforcement learning (MARL) settings, the centralized training with decentralized execution (CTDE) becomes customary recently due to the physical demand. However, the most dilemma is the inconsistency of jointly-trained policies and individually-optimized actions. In this work, we propose a novel value-based multi-objective learning approach, named Tchebycheff value decomposition optimization (TVDO), to overcome the above dilemma. In particular, a nonlinear Tchebycheff aggregation method is designed to transform the MARL task into multi-objective optimal counterpart by tightly constraining the upper bound of individual action-value bias. We theoretically prove that TVDO well satisfies the necessary and sufficient condition of individual global max (IGM) with no extra limitations, which exactly guarantees the consistency between the global and individual optimal action-value function. Empirically, in the climb and penalty game, we verify that TVDO represents precisely from global to individual value factorization with a guarantee of the policy consistency. Furthermore, we also evaluate TVDO in the challenging scenarios of StarCraft II micromanagement tasks, and extensive experiments demonstrate that TVDO achieves more competitive performances than several state-of-the-art MARL methods.

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