Parametric Logistic LCE Learner

Fits a four-parameter logistic learning curve $$f(b) = \ell + \frac{u - \ell}{1 + \exp(-k\,(b - b_0))}$$ to the per-batch surrogate performance. Captures S-shaped trajectories with a lower asymptote \(\ell\), an upper asymptote \(u\), a transition midpoint \(b_0\), and a steepness \(k > 0\). Decreasing trajectories are represented by upper < lower rather than by a negative rate.

The curve is fit on the task's lce_link scale. When predict_type = "se" the learner reports the epistemic Gauss-Newton delta-method standard error se_epistemic and the total predictive standard error se (adding the residual variance), both on the link scale; predictive quantiles are the exact Normal quantiles of that predictive.

Creates a new instance of this learner.

Parameters

• lower_init, upper_init, midpoint_init, rate_init :: numeric(1)
  Initial values for lower, upper, midpoint, and rate. Defaults are derived from the training data when unset.

• rate_lower :: numeric(1)
  Lower bound for rate. Initialized to 1e-6.

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