$\epsilon$ is supposed to be a random variable with a mean of 0.

University of Michigan - Ann Arbor

The error term $\epsilon$ indicates the residual of fitted values compared to the observed outcomes, i.e., $\epsilon$ accounts for variation in $Y$ that cannot be explained by the estimated function $f$:
$$Y=f(X)+\epsilon$$ 

$\epsilon$ in supervised statistical learning

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

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