Robust low-rank tensor regression via truncation and adaptive Huber loss

This paper investigates robust low-rank tensor regression with only finite $(1+\epsilon)$-th moment noise based on the generalized tensor estimation framework proposed by Han et al. (2022). The theoretical result shows that when $\epsilon \geq 1$, the robust estimator possesses the minimax optimal rate. While $1> \epsilon>0$, the rate is slower than the deviation bound of sub-Gaussian tails.