Since the time variable can be treated as a normal feature in classification, why not using more powerful classification methods (such as, C4.5, SVM) to predict the occurrence of an event? Why lots of people still use the classic but old Cox model?

In case of the right-censoring data, since the time would change for an instances, so I think same object with different time values could be treated as two different instances in classification. Is this OK? Is there are some highly-cited paper on this topic? Thank you!

The learning rate is a parameter that determines how much an updating step influences the current value of the weights. While weight decay is an additional term in the weight update rule that causes the weights to exponentially decay to zero, if no other update is scheduled.

So let's say that we have a cost or error function $E(\mathbf{w})$ that we want to minimize. Gradient descent tells us to modify the weights $\mathbf{w}$ in the direction of steepest descent in $E$:
\begin{equation}
w_i \leftarrow w_i-\eta\frac{\partial E}{\partial w_i},
\end{equation}
where $\eta$ is the learning rate, and if it's large you will have a correspondingly large modification of the weights $w_i$ (in general it shouldn't be too large, otherwise you'll overshoot the local minimum in your cost function).

In order to effectively limit the number of free parameters in your model so as to avoid over-fitting, it is possible to regularize the cost function. An easy way to do that is by introducing a zero mean Gaussian prior over the weights, which is equivalent to changing the cost function to $\widetilde{E}(\mathbf{w})=E(\mathbf{w})+\frac{\lambda}{2}\mathbf{w}^2$. In practice this penalizes large weights and effectively limits the freedom in your model. The regularization parameter $\lambda$ determines how you trade off the original cost $E$ with the large weights penalization.

Applying gradient descent to this new cost function we obtain:
\begin{equation}
w_i \leftarrow w_i-\eta\frac{\partial E}{\partial w_i}-\eta\lambda w_i.
\end{equation}
The new term $-\eta\lambda w_i$ coming from the regularization causes the weight to decay in proportion to its size.
