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What is the role of the learning rate (shrinkage) in GBM?

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Answer

  • Each new tree's contribution is scaled by eta in (0, 1] before being added: Fm+1  =  Fm  +  η    hmF_{m + 1}\; = \;F_{m}\; + \;\eta\; \cdot \;h_{m}.
  • Smaller eta needs more trees (nestimators)(n_{\mathrm{estimators}}) but generalizes better — analogous to a slow, cautious descent that lets many complementary trees contribute rather than one big correction.
  • Rule of thumb: η  =  0.050.1\eta\; = \;0.05 - 0.1 with a few hundred to a few thousand trees, using early stopping on validation.
  • Increasing eta trades quality for training time.
Check yourself — multiple choice
  • eta scales the target
  • eta scales each tree's contribution — smaller eta + more trees generalizes better
  • eta must always be 1
  • eta is only used for regression

Shrinkage: smaller eta ⇒ more trees needed ⇒ better generalization.

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