The global capacity for mineral processing must expand rapidly to meet the demand for critical minerals, which are essential for building the clean energy technologies necessary to mitigate climate change. However, the efficiency of mineral processing is severely limited by uncertainty, which arises from both the variability of feedstock and the complexity of process dynamics. To optimize mineral processing circuits under uncertainty, we introduce an AI-driven approach that formulates mineral processing as a Partially Observable Markov Decision Process (POMDP). We demonstrate the capabilities of this approach in handling both feedstock uncertainty and process model uncertainty to optimize the operation of a simulated, simplified flotation cell as an example. We show that by integrating the process of information gathering (i.e., uncertainty reduction) and process optimization, this approach has the potential to consistently perform better than traditional approaches at maximizing an overall objective, such as net present value (NPV). Our methodological demonstration of this optimization-under-uncertainty approach for a synthetic case provides a mathematical and computational framework for later real-world application, with the potential to improve both the laboratory-scale design of experiments and industrial-scale operation of mineral processing circuits without any additional hardware.