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3 questions with no upvoted or accepted answers
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inequality in a shape of inclusion exclusion formula
I have two inequalities to show, both of which describe some probabilities. First I know how to handle, and it follows from applying arithmetic-harmonic mean inequality:
consider 9 numbers $a_1,a_2,...
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2
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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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-1
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Transforming random variables for having good property?
For arbitrary functions $A$ and $B$ and independent random variables $X$ and $Y$, assume that
\begin{align}
\Omega&\triangleq \{(x,y): A(x,y)=1\},\\
\Lambda&\triangleq \{x: B(x)=1\}.
\end{...
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