Multi-parameter linear regression

Assumes there is a linear relationship between inputs and outputs, where there are several trainable parameters $(a_{1}, a_{2}, . . ., a_{k}, b)$ to be chosen

y_{i} \approx \sum_{k = 1}^{K} a_{k} x_{i}^{k} + b

Optimisation problem to training is then:

(a_{1}, a_{2}, . . ., a_{k}, b) = \underset{a_{1}, . . ., a_{K}, b}{arg min} \frac{1}{N} \sum_{i = 1}^{N} [\sum_{k = 1}^{K} a_{k} x_{i}^{k} + b - y_{i})]