Relationship between line search and least mean square algorithm

[edwardnash]

Hi there,
I am going thru basics of optimization and I see line search being used in many sophisticated optimization algorithms. From what I understand, it works by taking the derivative at a point and moves in a direction that minimizes the function. I have earlier experience using least mean square(LMS) algorithm which does a similar thing and is widely used in linear regression and neural networks. I was wondering if LMS comes under the family of line search algorithms or there is a very fundamental difference I am missing.thanks!

 

[jvicens]

Hello,

Thank you for your question. Line search is indeed a commonly used technique in optimization algorithms. It involves finding the optimal step size along a specific direction to minimize a function. This is usually done by taking the derivative at a specific point and moving in a direction that reduces the function value.

The least mean square (LMS) algorithm is a specific type of gradient descent algorithm that is commonly used in linear regression and neural networks. It also involves finding the optimal step size along a specific direction to minimize a cost function. Therefore, it can be considered as a form of line search algorithm.

However, there are some fundamental differences between LMS and other line search algorithms. LMS is specifically designed for convex cost functions and uses a fixed step size, while other line search algorithms can handle non-convex functions and adaptively adjust the step size during the optimization process.

In summary, LMS can be considered as a line search algorithm, but it is a specific type with its own unique characteristics. I hope this helps clarify any confusion. Let me know if you have any further questions.