This paper presents a framework to describe and explain human-machine collaborative design focusing on Design Space Exploration (DSE), which is a popular method used in the early design of complex systems with roots in the well-known design as exploration paradigm. The human designer and a cognitive design assistant are both modeled as intelligent agents, with an internal state (e.g., motivation, cognitive workload), a knowledge state (separated in domain, design process, and problem specific knowledge), an estimated state of the world (i.e., status of the design task) and of the other agent, a hierarchy of goals (short-term and long-term, design and learning goals) and a set of long-term attributes (e.g., Kirton’s Adaption-Innovation inventory style, risk aversion). The framework emphasizes the relation between design goals and learning goals in DSE, as previously highlighted in the literature (e.g., Concept-Knowledge theory, LinD model) and builds upon the theory of common ground from human-computer interaction (e.g., shared goals, plans, attention) as a building block to develop successful assistants and interactions. Recent studies in human-AI collaborative DSE are reviewed from the lens of the proposed framework, and some new research questions are identified. This framework can help advance the theory of human-AI collaborative design by helping design researchers build promising hypotheses, and design studies to test these hypotheses that consider most relevant factors.