The Power of the Pareto Front: Balancing Uncertain Rewards for Adaptive Experimentation in scanning probe microscopy

Automated experimentation has the potential to revolutionize scientific discovery, but its effectiveness depends on well-defined optimization targets, which are often uncertain or probabilistic in real-world settings. In this work, we demonstrate the application of Multi-Objective Bayesian Optimization (MOBO) to balance multiple, competing rewards in autonomous experimentation. Using scanning probe microscopy (SPM) imaging, one of the most widely used and foundational SPM modes, we show that MOBO can optimize imaging parameters to enhance measurement quality, reproducibility, and efficiency. A key advantage of this approach is the ability to compute and analyze the Pareto front, which not only guides optimization but also provides physical insights into the trade-offs between different objectives. Additionally, MOBO offers a natural framework for human-in-the-loop decision-making, enabling researchers to fine-tune experimental trade-offs based on domain expertise. By standardizing high-quality, reproducible measurements and integrating human input into AI-driven optimization, this work highlights MOBO as a powerful tool for advancing autonomous scientific discovery.