Review for NeurIPS paper: Adaptive Importance Sampling for Finite-Sum Optimization and Sampling with Decreasing Step-Sizes

Weaknesses: (W1) - The contributions of the paper are very close from the one of [12]. Indeed, it takes ideas from [12] to restrict the analysis on a simplex that we can control. Moreover, it doesn't clearly put forward the novelty of the bound on dynamic regret compared to the one of [18]. For instance, the following sentence serves to define a key quantity in the authors development: ''For each i [N ], denote by hti the last observed gradient of fi at time t, with h1i initialized arbitrarily'' Unfortunately, it is quite unclear as two readers might understand something different. In the same line of comments, the proof of Lemma 3 is very confusing.