Log-cosh Loss

• Similar to Huber Loss but without the hyperparameter $\delta$
• It also behaves like squared error for small values and absolute error for larger values.

[!def] Log-cosh Loss Formula
$$
L = \sum_i log(cosh(\hat{y_i} - y_i))
$$

Pros:

1. Benefits of Huber Loss with twice differentiability
2. Fewer computation than Huber Loss

Cons:

1. Compared to Huber Loss, more complex Derivative