Using a different proof technique, the results are extended to the class of spectral risk measures having a bounded risk spectrum.

We call that σ -algebra history before n . Identification tasks We focus on best arm identification (BAI).

The structure of the appendix mainly follows the roadmap of the proof described in Section 4.4. In Appendix A, we define the characterizable population risk function in (31) to approximate the objective function. Also, some notations to simplify the analysis are introduced in Appendix A, and we recommend the readers to refer to Table 3 for the major notations used in the proofs. Instead, in this paper, we consider multi-layer cases and need to derive a lower bound for the Hessian matrix for all the layers. Instead, the input of the intermediate layer cannot be proved to be Gaussian but belong to sub-Gaussian distribution.

This was proposed and named by Tibshirani et al. (2005),

Section 2.2 for the precise formulation) and to address issue (b) by developing a tighter upper bound

For instance, researchers are examining the gene network derived from the gene expression data of patients to investigate a rare disease.