Author is also affiliated with RaySearch Laboratories. Here is an incomplete list. Our proof consist of two parts. There are two cases to consider. There are two cases to consider.

Modern machine learning systems are able to learn extremely complicated relations from data.

Manifold clustering is an important problem in motion and video segmentation, natural image clustering, and other applications where high-dimensional data lie on multiple, low-dimensional, nonlinear manifolds.

Hence, the following research questions arise: What is the optimal regret lower bound in contextual MNL bandits?

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning.

Then momentum acceleration is also introduced into our dual accelerating update step.