Jason, the scientist, tries to figure out the relationship between the temperature and the reaction rate for h2 and o2. he knows the relationship (a. k.a, reaction function) is k = a * ∗ −/ , k is the reaction rate, t is the temperature he decides to use gradient descent to find out the value for a, b and c. jason gathers all past lab results, 10,000 records in total. each record has the format of (t, k’, ku) where k’ is the reaction rate measured in the lab test and ku is the uncertainty of k’. jason uses the loss function below.
l (t, a, b, c ) = 1/20,000 \sum( −′)/ )^2
k(t, a,b, c) is the value calculated by the reaction function. k’ is the reaction rate measured in a lab result. ku is the uncertainty of k’
1. you can assume the learning rates for a, b and c are la, lb and lc respectively. write the update functions for parameter a, b and c for the process of gradient descent. explain why.
2. jason knows that the approximate values of a, b and c, which are 10−10 , −0.1 60. the range of temperature for the lab results is [300, 2000]. ′ 10%. choose the initial values for the learning rates la, lb and lc. explain why.
3. jason finds that if he choose different initial values of a, b and c, he often gets different final results. explain why.