Hyperspectral imaging (HSI) captures a greater level of spectral detail than traditional optical imaging, making it a potentially valuable intraoperative tool when precise tissue differentiation is essential. Hardware limitations of current optical systems used for handheld real-time video HSI result in a limited focal depth, thereby posing usability issues for integration of the technology into the operating room. This work integrates a focus-tunable liquid lens into a video HSI exoscope, and proposes novel video autofocusing methods based on deep reinforcement learning. A first-of-its-kind robotic focal-time scan was performed to create a realistic and reproducible testing dataset. We benchmarked our proposed autofocus algorithm against traditional policies, and found our novel approach to perform significantly ($p<0.05$) better than traditional techniques ($0.070\pm.098$ mean absolute focal error compared to $0.146\pm.148$). In addition, we performed a blinded usability trial by having two neurosurgeons compare the system with different autofocus policies, and found our novel approach to be the most favourable, making our system a desirable addition for intraoperative HSI.