However, calculating the Laplacian spectrum can be expensive in a matrix base.

Covering option discovery has been developed to improve the exploration of RL in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. Given that joint state space grows exponentially with the number of agents in multi-agent systems, existing researches still relying on single-agent option discovery either become prohibitive or fail to directly discover joint options that improve the connectivity of the joint state space. In this paper, we show how to directly compute multi-agent options with collaborative exploratory behaviors while still enjoying the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph, based on which we can directly estimate its Fiedler vector using the Laplacian spectrum of individual agents' transition graphs. Further, considering that directly computing the Laplacian spectrum is intractable for tasks with infinite-scale state spaces, we further propose a deep learning extension of our method by estimating eigenfunctions through NN-based representation learning techniques. The evaluation on multi-agent tasks built with simulators like Mujoco, shows that the proposed algorithm can successfully identify multi-agent options, and significantly outperforms the state-of-the-art. Codes are available at: https://github.itap.purdue.edu/Clan-labs/Scalable

However, calculating the Laplacian spectrum can be expensive in a matrix base.

Covering option discovery has been developed to improve the exploration of RL in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. Given that joint state space grows exponentially with the number of agents in multi-agent systems, existing researches still relying on single-agent option discovery either become prohibitive or fail to directly discover joint options that improve the connectivity of the joint state space. In this paper, we show how to directly compute multi-agent options with collaborative exploratory behaviors while still enjoying the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph, based on which we can directly estimate its Fiedler vector using the Laplacian spectrum of individual agents' transition graphs. Further, considering that directly computing the Laplacian spectrum is intractable for tasks with infinite-scale state spaces, we further propose a deep learning extension of our method by estimating eigenfunctions through NN-based representation learning techniques.

The use of skills (a.k.a., options) can greatly accelerate exploration in reinforcement learning, especially when only sparse reward signals are available. While option discovery methods have been proposed for individual agents, in multi-agent reinforcement learning settings, discovering collaborative options that can coordinate the behavior of multiple agents and encourage them to visit the under-explored regions of their joint state space has not been considered. In this case, we propose Multi-agent Deep Covering Option Discovery, which constructs the multi-agent options through minimizing the expected cover time of the multiple agents' joint state space. Also, we propose a novel framework to adopt the multi-agent options in the MARL process. In practice, a multi-agent task can usually be divided into some sub-tasks, each of which can be completed by a sub-group of the agents. Therefore, our algorithm framework first leverages an attention mechanism to find collaborative agent sub-groups that would benefit most from coordinated actions. Then, a hierarchical algorithm, namely HA-MSAC, is developed to learn the multi-agent options for each sub-group to complete their sub-tasks first, and then to integrate them through a high-level policy as the solution of the whole task. This hierarchical option construction allows our framework to strike a balance between scalability and effective collaboration among the agents. The evaluation based on multi-agent collaborative tasks shows that the proposed algorithm can effectively capture the agent interactions with the attention mechanism, successfully identify multi-agent options, and significantly outperforms prior works using single-agent options or no options, in terms of both faster exploration and higher task rewards.

Covering skill (a.k.a., option) discovery has been developed to improve the exploration of RL in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. Given that joint state space grows exponentially with the number of agents in multi-agent systems, existing researches still relying on single-agent skill discovery either become prohibitive or fail to directly discover joint skills that improve the connectivity of the joint state space. In this paper, we propose multi-agent skill discovery which enables the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph, based on which we can directly estimate its Fiedler vector using the Laplacian spectrum of individual agents' transition graphs. Further, considering that directly computing the Laplacian spectrum is intractable for tasks with infinite-scale state spaces, we further propose a deep learning extension of our method by estimating eigenfunctions through NN-based representation learning techniques. The evaluation on multi-agent tasks built with simulators like Mujoco, shows that the proposed algorithm can successfully identify multi-agent skills, and significantly outperforms the state-of-the-art.

Covering option discovery has been developed to improve the exploration of reinforcement learning in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. However, these option discovery methods cannot be directly extended to multi-agent scenarios, since the joint state space grows exponentially with the number of agents in the system. Thus, existing researches on adopting options in multi-agent scenarios still rely on single-agent option discovery and fail to directly discover the joint options that can improve the connectivity of the joint state space of agents. In this paper, we show that it is indeed possible to directly compute multi-agent options with collaborative exploratory behaviors among the agents, while still enjoying the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph -- the Kronecker product of individual agents' state transition graphs, based on which we can directly estimate the Fiedler vector of the joint state space using the Laplacian spectrum of individual agents' transition graphs. This decomposition enables us to efficiently construct multi-agent joint options by encouraging agents to connect the sub-goal joint states which are corresponding to the minimum or maximum values of the estimated joint Fiedler vector. The evaluation based on multi-agent collaborative tasks shows that the proposed algorithm can successfully identify multi-agent options, and significantly outperforms prior works using single-agent options or no options, in terms of both faster exploration and higher cumulative rewards.