Doeblin Curves
Researchers have introduced the concept of a "Doeblin curve" to provide a more detailed characterization of multi-way contraction behavior in Markov kernels. This new approach offers non-vacuous contraction guarantees even for channels where the traditional Doeblin coefficient is zero. The Doeblin curve quantifies contraction across collections of input distributions at specific levels of divergence and power. The findings have applications in areas such as noisy iterative optimization, reliable computation with noisy circuits, and differential privacy for online iterative algorithms. AI
IMPACT Enhances theoretical understanding of information contraction, potentially improving algorithms in optimization and privacy.