# D20 - 7.2 The Naive Solution Gradient Ascent The simplest...

This preview shows pages 1–2. Sign up to view the full content.

7.2 The Naive Solution: Gradient Ascent The simplest numerical solution of a convex optimisation problem is obtained by gradient ascent, sometimes known as the steepest ascent algorithm. The algorithm starts with an initial estimate for the solution, denoted by α 0 , and then iteratively updates the vector following the steepest ascent path, that is moving in the direction of the gradient of W ( α ) evaluated at the position α t for update t + 1. At each iteration the direction of the update is determined by the steepest ascent strategy but the length of the step still has to be fixed. The length of the update is known as the learning rate . In the sequential or stochastic version, this strategy is approximated by evaluating the gradient for just one pattern at a time, and hence updating a single component α i t by the increment where the parameter η is the learning rate. If η is chosen carefully, the objective function will increase monotonically, and the average direction approximates the local gradient. One can

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern