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Bounds for $\sum_{t=1}^Tn_t(s_t)^{-\alpha}\mu(s_t)$ where $n_t(s) = \sum_{1 \le t' \le t} 1_{\{s_{t'}=s\}}$ for $s \in [k]$ and $\mu \in \Delta_k$

Disclaimer: I'm not certain this is the right venue for this post, but I'll give it a try... So trying prove some bounds in my ongoing work in theoretical reinforcement learning, I encountered the ...
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