Parametric Power-Law LCE Learner

Fits a three-parameter power-law learning curve $$f(b) = c + a\,b^{-k}$$ to the per-batch surrogate performance. Compared to LearnerLCEParametricExponential the power-law family decays more slowly, matching the heavier-tailed convergence often seen in sample-complexity bounds.

The curve is fit on the task's lce_link scale and standard errors and quantiles are computed exactly as for LearnerLCEParametricExponential (link-scale epistemic se_epistemic plus total predictive se).

Training batches with batch_nr <= 0 are not supported because \(b^{-k}\) is then undefined; such tasks raise an error.

Creates a new instance of this learner.

Parameters

• asymptote_init, amplitude_init, rate_init :: numeric(1)
  Initial values for c, a, and k.

• rate_lower :: numeric(1)
  Lower bound for the decay exponent k. Initialized to 1e-6.

• maxit :: integer(1)
  Maximum optim iterations. Initialized to 500.