Information is sent over a noisy underwater acoustic channel where the noisy signal _[x_1,...,x_d]^T is collected as input vector X and the transmitted signal y is predicted using a linear regression filter, i.e., y=w^TX+b. Consider the following function as stochastic loss,

l(x,X_i,y_i) = log (1+||y_i - w^TX_i||²)

Derive the SGD update for vector w that minimizes the loss.