  A brain-computer interface (BCI) is a technology that enables direct
communication between the brain and an external device or computer system. It
allows individuals to interact with the device using only their thoughts, and
holds immense potential for a wide range of applications in medicine,
rehabilitation, and human augmentation. An electroencephalogram (EEG) and
event-related potential (ERP)-based speller system is a type of BCI that allows
users to spell words without using a physical keyboard, but instead by
recording and interpreting brain signals under different stimulus presentation
paradigms. Conventional non-adaptive paradigms treat each word selection
independently, leading to a lengthy learning process. To improve the sampling
efficiency, we cast the problem as a sequence of best-arm identification tasks
in multi-armed bandits. Leveraging pre-trained large language models (LLMs), we
utilize the prior knowledge learned from previous tasks to inform and
facilitate subsequent tasks. To do so in a coherent way, we propose a
sequential top-two Thompson sampling (STTS) algorithm under the
fixed-confidence setting and the fixed-budget setting. We study the theoretical
property of the proposed algorithm, and demonstrate its substantial empirical
improvement through both synthetic data analysis as well as a P300 BCI speller
simulator example.
