In this position paper, we review the eclectic recent history of academic and artistic works involving computational systems for humor generation, and focus specifically on live performance. We make the case that AI comedy should be evaluated in live conditions, in front of audiences sharing either physical or online spaces, and under real-time constraints. We further suggest that improvised comedy is therefore the perfect substrate for deploying and assessing computational humor systems. Using examples of successful AI-infused shows, we demonstrate that live performance raises three sets of challenges for computational humor generation: 1) questions around robotic embodiment, anthropomorphism and competition between humans and machines, 2) questions around comedic timing and the nature of audience interaction, and 3) questions about the human interpretation of seemingly absurd AI-generated humor. We argue that these questions impact the choice of methodologies for evaluating computational humor, as any such method needs to work around the constraints of live audiences and performance spaces. These interrogations also highlight different types of collaborative relationship of human comedians towards AI tools.