How do you get leadership buy-in for AI investment when they're sceptical of the hype?

Our senior leadership team watched the RPA wave, invested heavily, and got mediocre returns. They're now extremely cautious about AI. I believe there are genuine productivity opportunities — particularly in document processing and customer service — but I can't get a meaningful budget approved. How do innovation leaders make the case for AI investment to a leadership team that has been burned before and is appropriately sceptical of technology hype?