GAM LCE Learner

Fits an unconstrained smoothing spline to the per-batch performance via mgcv::gam() with a single smooth s(batch_nr, k = k, bs = bs), estimated by REML. This is the classic "GAM extrapolation with confidence bands" workflow for learning-curve extrapolation. Unlike LearnerLCESplineMonotone it imposes no monotonicity, so it can also track non-monotone curves – at the price of less stable extrapolation.

The curve is fit on the task's lce_link scale. Extrapolation beyond the training-batch range extends the spline basis (linearly beyond the boundary knots for the "cr" basis), so long-horizon forecasts can drift; the pointwise standard errors grow accordingly.

When predict_type = "se" the learner returns the spline's pointwise standard errors (as reported by mgcv::predict.gam()) as the epistemic se_epistemic and adds the residual variance back to form the total predictive se, both on the link scale.

At least four distinct batches are required; k is clamped to at most n_batches - 1 to keep the fit identifiable.

Creates a new instance of this learner.

Parameters

• k :: integer(1) | NULL
  Basis dimension passed to mgcv::s(). Defaults to NULL, which uses min(6, n_batches - 1). Floored at 3 and clamped to at most n_batches - 1 at training time.

• bs :: character(1)
  Spline basis: "cr" (cubic regression spline, default; extrapolates linearly beyond the boundary knots) or "tp" (thin plate).