# Quention about the initialization of Exponentially Weighted Averages

**URL:** <https://community.deeplearning.ai/t/quention-about-the-initialization-of-exponentially-weighted-averages/114861>\
**Category:** Improving Deep Neural Networks: Hyperparameter tun\
**Tags:** coursera-platform\
**Created:** [April 1, 2022, 6:53am UTC](https://community.deeplearning.ai/t/quention-about-the-initialization-of-exponentially-weighted-averages/114861 "2022-04-01T06:53:01Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![qiu](https://avatars.discourse-cdn.com/v4/letter/q/ed8c4c/32.png) [@qiu](https://community.deeplearning.ai/u/qiu)\
**Post date:** [April 1, 2022, 6:53am UTC](https://community.deeplearning.ai/t/quention-about-the-initialization-of-exponentially-weighted-averages/114861/1 "2022-04-01T06:53:01Z")

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In the course, the ewa is initialized to v(0)=0, and v(i)=0.9_v(i-1)+0.1_theta(i). The problem is that the first few v will be very close to zero.

So in later video, there is a bias correction formula: vi/(1-beta\*\*t)

My question is: why not set v(1)=theta(1), and v(i)=0.9\*v(i-1)+0.1theta(i).

What’s the difference between this two kind of initialization. Why introduce such a complex correction formula instead of just set v(1)=theta(1)

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**Author:** ![nramon](https://sea1.discourse-cdn.com/dlai/user_avatar/community.deeplearning.ai/nramon/32/129097_2.png) [@nramon](https://community.deeplearning.ai/u/nramon)\
**Post date:** [April 21, 2022, 9:13am UTC](https://community.deeplearning.ai/t/quention-about-the-initialization-of-exponentially-weighted-averages/114861/2 "2022-04-21T09:13:08Z")

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Hi, @qiu:

Sorry for the late reply 😓

The alternative you propose is perfectly fine, but whether you initialize to 0 or `theta(1)`, the first values of the moving average will be biased towards this constant (this may be acceptable for your use case). The formula from the [later video](https://www.coursera.org/learn/deep-neural-network/lecture/XjuhD/bias-correction-in-exponentially-weighted-averages) tries to correct this initial bias.

Did that make sense?

Hope you’re enjoying the specialization 🙂