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sup and max in the one-period problem #3

Open k2pctdn opened 3 weeks ago

k2pctdn commented 3 weeks ago

image In file Chap11_July_8.pdf, Chapter 1, page 30, The one-period problem: a fundamental building block, footnote no. 26 states:

"When maximizing over a non-finite set, we write sup even when the sup is attained to emphasize that the set is not finite."

However, I believe it would be more accurate as follows:

"When maximizing over a non-finite set, we write sup even when the max is attained to emphasize that the set is not finite."

Also, on the same page, the paragraph begins with, "To see this, first note that (1.48) is greater than or equal to (1.49) [...]". I am not entirely sure, but from my understanding, for a finite set, the weighted average value cannot exceed the largest element in the set. Therefore, (1.48) cannot be "greater than or equal to (1.49)", but "less than or equal to (1.49)".

(Please refer to the screenshot for more details.)

P.S. Thank you very much for updating the 1995 book! It has greatly enhanced my understanding of MDPs. I look forward to the new book's release and its valuable insights.

martyput commented 3 weeks ago

Thank you. Very helpful. Yes we wrestled with this point.

Marty

From: Quang-Khai Tran @.> Reply-To: martyput/MDP_book @.> Date: Wednesday, October 30, 2024 at 09:48 To: martyput/MDP_book @.> Cc: Subscribed @.> Subject: [martyput/MDP_book] sup and max in the one-period problem (Issue #3)

[CAUTION: Non-UBC Email]

image.png (view on web)https://github.com/user-attachments/assets/bca994af-5bae-47e4-b6ef-b95883d891b3 In file Chap11_July_8.pdf, Chapter 1, page 30, The one-period problem: a fundamental building block, footnote no. 26 states:

"When maximizing over a non-finite set, we write sup even when the sup is attained to emphasize that the set is not finite."

However, I believe it would be more accurate as follows:

"When maximizing over a non-finite set, we write sup even when the max is attained to emphasize that the set is not finite."

(Please refer to the screenshot for more details.)

P.S. Thank you very much for updating the 1995 book! It has greatly enhanced my understanding of MDPs. I look forward to the new book's release and its valuable insights.

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