Collecting diverse near-optimal samples via nested Thompson sampling

Self-driving laboratories (SDLs) that combine automated experiments with machine learning have accelerated data-driven discovery. Although Bayesian optimization (BO) is widely used in SDLs to autonomously propose experimental conditions, many real systems require sampling diverse near-optimal candidates rather than identifying a single optimum. We propose nested Thompson sampling (NTS), a batch BO method that enhances diversity by incorporating the concept of nested sampling. In NTS, regions where the posterior exceeds a likelihood threshold are uniformly sampled, enabling exploration of multiple promising regions while requiring only one hyperparameter, that is, the threshold schedule. Benchmark studies using materials datasets demonstrated that NTS achieves higher sample diversity than a conventional batch BO method. Furthermore, the application of NTS to automated electrolyte exploration in an SDL successfully produced diverse experimental samples. The NTS algorithm is implemented in the NIMO package, providing a practical framework for autonomous and diverse materials exploration.