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This paper investigates robust low-rank tensor regression with only finite$(1+\epsilon)$-th moment noise based on the generalized tensor estimationframework 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 ofsub-Gaussian tails.

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