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))


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


  1. Compared to Huber Loss, more complex Derivative

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