While there is a widespread belief that artificial general intelligence (AGI) -- or even superhuman AI -- is imminent, complex problems in expert domains are far from being solved. We argue that such problems require human-AI cooperation and that the current state of the art in generative AI is unable to play the role of a reliable partner due to a multitude of shortcomings, including inability to keep track of a complex solution artifact (e.g., a software program), limited support for versatile human preference expression and lack of adapting to human preference in an interactive setting. To address these challenges, we propose HAI-Co2, a novel human-AI co-construction framework. We formalize HAI-Co2 and discuss the difficult open research problems that it faces. Finally, we present a case study of HAI-Co2 and demonstrate its efficacy compared to monolithic generative AI models.
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