  The focus of the paper is functional output regression (FOR) with convoluted
losses. While most existing work consider the square loss setting, we leverage
extensions of the Huber and the $\epsilon$-insensitive loss (induced by infimal
convolution) and propose a flexible framework capable of handling various forms
of outliers and sparsity in the FOR family. We derive computationally tractable
algorithms relying on duality to tackle the resulting tasks in the context of
vector-valued reproducing kernel Hilbert spaces. The efficiency of the approach
is demonstrated and contrasted with the classical squared loss setting on both
synthetic and real-world benchmarks.

Machine Learning;Machine Learning