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Covering skill (a.k.a., option) discovery has been developed to improve theexploration of RL in single-agent scenarios with sparse reward signals, throughconnecting the most distant states in the embedding space provided by theFiedler vector of the state transition graph. Given that joint state spacegrows exponentially with the number of agents in multi-agent systems, existingresearches still relying on single-agent skill discovery either becomeprohibitive or fail to directly discover joint skills that improve theconnectivity of the joint state space. In this paper, we propose multi-agentskill discovery which enables the ease of decomposition. Our key idea is toapproximate the joint state space as a Kronecker graph, based on which we candirectly estimate its Fiedler vector using the Laplacian spectrum of individualagents' transition graphs. Further, considering that directly computing theLaplacian spectrum is intractable for tasks with infinite-scale state spaces,we further propose a deep learning extension of our method by estimatingeigenfunctions through NN-based representation learning techniques. Theevaluation on multi-agent tasks built with simulators like Mujoco, shows thatthe proposed algorithm can successfully identify multi-agent skills, andsignificantly outperforms the state-of-the-art. Codes are available at:https://github.itap.purdue.edu/Clan-labs/Scalable_MAOD_via_KP.

Scalable Multi-agent Covering Option Discovery based on Kronecker Graphs