Dialogue-based human-AI collaboration can revolutionize collaborative problem-solving, creative exploration, and social support. To realize this goal, the development of automated agents proficient in skills such as negotiating, following instructions, establishing common ground, and progressing shared tasks is essential. This survey begins by reviewing the evolution of dialogue management paradigms in collaborative dialogue systems, from traditional handcrafted and information-state based methods to AI planning-inspired approaches. It then shifts focus to contemporary data-driven dialogue management techniques, which seek to transfer deep learning successes from form-filling and open-domain settings to collaborative contexts. The paper proceeds to analyze a selected set of recent works that apply neural approaches to collaborative dialogue management, spotlighting prevailing trends in the field. This survey hopes to provide foundational background for future advancements in collaborative dialogue management, particularly as the dialogue systems community continues to embrace the potential of large language models.

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