Temporal Point Processes (TPPs), especially the Hawkes process, are commonly used for modeling asynchronous event-type big data, such as financial transactions and user behaviors in social networks. Due to the strong fitting ability of neural networks, various neural point processes are proposed, among which the neural Hawkes processes based on self-attention, such as the Transformer Hawkes Process (THP), achieve distinct performance improvement. Although the THP has gained popular applications, it still suffers from low accuracy and unstable performance in sequence prediction tasks when training on history sequences and inferencing about the future, which is a prevalent paradigm in realistic sequence analysis. Conventional THP and its variants generally adopt sinusoid embedding in transformers, which also shows severe performance sensitivity to temporal change or noise by empirical study. To deal with the above problems, we propose a new Rotary position embedding-based THP (RoTHP), which for the first time encodes the temporal information in the Hawkes process with rotary embedding, and then constructs the intensity function adaptively. Notably, we show the translation invariance property of the RoTHP induced by the relative time encoding when coupled with the Hawkes process theoretically, and illustrate its sequence prediction flexibility. Extensive experiments are conducted, which demonstrate that the proposed RoTHP can be better generalized when dealing with sequence data with timestamp translations or noise, and show its superior performance in sequence prediction tasks.

The Thresholding Bandit (TB) problem is a popular sequential decision-making problem, which aims at identifying the systems whose means are greater than a threshold. Instead of working on the upper bound of a loss function, our approach stands out from conventional practices by directly minimizing the loss itself. Leveraging the large deviation theory, we firstly provide an asymptotically optimal allocation rule for the TB problem, and then propose a parameter-free Large Deviation (LD) algorithm to make the allocation rule implementable. Central limit theorem-based Large Deviation (CLD) algorithm is further proposed as a supplement to improve the computation efficiency using normal approximation. Extensive experiments are conducted to validate the superiority of our algorithms compared to existing methods, and demonstrate their broader applications to more general distributions and various kinds of loss functions.