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The formatting here was infelicitous. This is also not perfect but it's definitely better.
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edit approved Nov 6, 2020 at 0:17
Community Bot
edit approved Nov 6, 2020 at 0:17
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I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis' 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$$$ \begin{array}l \text{(The Pinelis' 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \\ \text{be a random process satisfying } \mathbb{E}[X_t\mid X_1,\dots,X_{t−1} ] = 0 \text{ and} \\ \|X_t\| ≤ M. \text{ Then } \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. \end{array} $$

Nowhere in Pinelis' 1994 paper is this inequality mentioned.

So I ask myself, does this inequality really exist? Do you know it?

I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis' 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$

Nowhere in Pinelis' 1994 paper is this inequality mentioned.

So I ask myself, does this inequality really exist? Do you know it?

I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \begin{array}l \text{(The Pinelis' 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \\ \text{be a random process satisfying } \mathbb{E}[X_t\mid X_1,\dots,X_{t−1} ] = 0 \text{ and} \\ \|X_t\| ≤ M. \text{ Then } \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. \end{array} $$

Nowhere in Pinelis' 1994 paper is this inequality mentioned.

So I ask myself, does this inequality really exist? Do you know it?

grammar corrections, formatting
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Glorfindel
Glorfindel
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Does PinelisPinelis' inequality (1994) exist?

I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis'sPinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis's 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$$$ \mbox{(The Pinelis' 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$

At no timeNowhere in Pinelis' 1994 paper (https://projecteuclid.org/download/pdf_1/euclid.aop/1176988477Pinelis' 1994 paper) is this inequality mentioned.

So I ask myself, does this inequality really exist? doDo you know it?

Does Pinelis inequality (1994) exist?

I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis's 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis's 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$

At no time in Pinelis' 1994 paper (https://projecteuclid.org/download/pdf_1/euclid.aop/1176988477) is this inequality mentioned.

So I ask myself, does this inequality really exist? do you know it?

Does Pinelis' inequality (1994) exist?

I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis' 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$

Nowhere in Pinelis' 1994 paper is this inequality mentioned.

So I ask myself, does this inequality really exist? Do you know it?

a grammar fix
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edit approved Nov 3, 2020 at 19:42
Ross Presser
edit approved Nov 3, 2020 at 19:42
Ross Presser
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I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis's 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I did not was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis's 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$

At no time in Pinelis' 1994 paper (https://projecteuclid.org/download/pdf_1/euclid.aop/1176988477) is this inequality mentioned.

So I ask myself, does this inequality really exist? do you know it?

I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis's 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I did not was able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis's 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$

At no time in Pinelis' 1994 paper (https://projecteuclid.org/download/pdf_1/euclid.aop/1176988477) is this inequality mentioned.

So I ask myself, does this inequality really exist? do you know it?

I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis's 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \mbox{(The Pinelis's 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \mbox{ be a random process satisfying } \mathbb{E}[X_t|X_1,\dots,X_{t−1} ] = 0 \mbox{ and } \|X_t\| ≤ M. \mbox{ Then }, \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. $$

At no time in Pinelis' 1994 paper (https://projecteuclid.org/download/pdf_1/euclid.aop/1176988477) is this inequality mentioned.

So I ask myself, does this inequality really exist? do you know it?

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K.J Fogang Fokoa
K.J Fogang Fokoa
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