Securing coordination between AI agent and teammates (human players or AI agents) in contexts involving unfamiliar humans continues to pose a significant challenge in Zero-Shot Coordination. The issue of cooperative incompatibility becomes particularly prominent when an AI agent is unsuccessful in synchronizing with certain previously unknown partners. Traditional algorithms have aimed to collaborate with partners by optimizing fixed objectives within a population, fostering diversity in strategies and behaviors. However, these techniques may lead to learning loss and an inability to cooperate with specific strategies within the population, a phenomenon named cooperative incompatibility in learning. In order to solve cooperative incompatibility in learning and effectively address the problem in the context of ZSC, we introduce the Cooperative Open-ended LEarning (COLE) framework, which formulates open-ended objectives in cooperative games with two players using perspectives of graph theory to evaluate and pinpoint the cooperative capacity of each strategy. We present two practical algorithms, specifically COLESV and COLER, which incorporate insights from game theory and graph theory. We also show that COLE could effectively overcome the cooperative incompatibility from theoretical and empirical analysis. Subsequently, we created an online Overcooked human-AI experiment platform, the COLE platform, which enables easy customization of questionnaires, model weights, and other aspects. Utilizing the COLE platform, we enlist 130 participants for human experiments. Our findings reveal a preference for our approach over state-of-the-art methods using a variety of subjective metrics. Moreover, objective experimental outcomes in the Overcooked game environment indicate that our method surpasses existing ones when coordinating with previously unencountered AI agents and the human proxy model. Our code and demo are publicly available at https://sites.google.com/view/cole-2023.

Zero-shot coordination in cooperative artificial intelligence (AI) remains a significant challenge, which means effectively coordinating with a wide range of unseen partners. Previous algorithms have attempted to address this challenge by optimizing fixed objectives within a population to improve strategy or behaviour diversity. However, these approaches can result in a loss of learning and an inability to cooperate with certain strategies within the population, known as cooperative incompatibility. To address this issue, we propose the Cooperative Open-ended LEarning (COLE) framework, which constructs open-ended objectives in cooperative games with two players from the perspective of graph theory to assess and identify the cooperative ability of each strategy. We further specify the framework and propose a practical algorithm that leverages knowledge from game theory and graph theory. Furthermore, an analysis of the learning process of the algorithm shows that it can efficiently overcome cooperative incompatibility. The experimental results in the Overcooked game environment demonstrate that our method outperforms current state-of-the-art methods when coordinating with different-level partners. Our demo is available at https://sites.google.com/view/cole-2023.