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This paper proposes the Decentralized Multi-Critic Actor Learning (DMultiCriticAL) method for quadruped robots to overcome the multi-task gradient conflict in multi-gait learning. In this method, each leg joint angle of quadruped robots is served as the action space of decentralized learning agents rather than learning directly to control all robot joint angles. Because of the high similarity in quadruped robot local action space, the DMultiCriticAL method can avoid the multi-task gradient conflict in multi-gait learning. Compared with the conventional multi-task learning method, we exploit the decentralized learning systems to limit the useless exploration of environments by agent, not design complex reward functions to track the multi-gait reference motion trajectory. This also means we can avoid the suboptimal reference motion trajectory design. Our experiment results show that the multi-gait motion controller based on the DMultiCriticAL method can yield more stable locomotion without complex reward function designs.