Stabilizing black-box algorithms through task-oriented randomization

As black-box models become foundational to modern research, ensuring their stability is paramount for the realization of trustworthy artificial intelligence. The inherent diversity of inputs - ranging from structured Gaussian distributions to complex data with unknown structures - poses a significant challenge: how to stabilize black-box outputs while effectively leveraging available prior information. This paper introduces a task-oriented randomization methodology that adaptively tailors its strategy to the underlying generative mechanisms of the input data, specifically addressing unstructured complexities. A comprehensive suite of stability guarantees is proposed. Beyond establishing rigorous theoretical foundations for stability, the research provides a detailed analysis of the intrinsic trade-off between stability and exploration. Motivated by the architecture of Large Language Models, the framework is further extended to top-k ranking problems. The validity and effectiveness of the proposal are demonstrated through extensive numerical simulations and applications to the real-world dataset.