Reinforcement learning has significant applications for multi-agent systems, especially in unknown dynamic environments. However, most multi-agent reinforcement learning (MARL) algorithms suffer from such problems as exponential computation complexity in the joint state-action space, which makes it difficult to scale up to realistic multi-agent problems. In this paper, a novel algorithm named negotiation-based MARL with sparse interactions (NegoSI) is presented. In contrast to traditional sparse-interaction based MARL algorithms, NegoSI adopts the equilibrium concept and makes it possible for agents to select the non-strict Equilibrium Dominating Strategy Profile (non-strict EDSP) or Meta equilibrium for their joint actions. The presented NegoSI algorithm consists of four parts: the equilibrium-based framework for sparse interactions, the negotiation for the equilibrium set, the minimum variance method for selecting one joint action and the knowledge transfer of local Q-values. In this integrated algorithm, three techniques, i.e., unshared value functions, equilibrium solutions and sparse interactions are adopted to achieve privacy protection, better coordination and lower computational complexity, respectively. To evaluate the performance of the presented NegoSI algorithm, two groups of experiments are carried out regarding three criteria: steps of each episode (SEE), rewards of each episode (REE) and average runtime (AR). The first group of experiments is conducted using six grid world games and shows fast convergence and high scalability of the presented algorithm. Then in the second group of experiments NegoSI is applied to an intelligent warehouse problem and simulated results demonstrate the effectiveness of the presented NegoSI algorithm compared with other state-of-the-art MARL algorithms.
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