Parametric Exponential LCE Learner

Fits a three-parameter exponential learning curve $$f(b) = c + a \exp(-k\,b)$$ to the per-batch surrogate performance. Suitable both for performance measures that grow to an asymptote (a ends up negative) and for loss measures that decay to an asymptote (a ends up positive).

The curve is fit on the task's lce_link scale, so for a non-identity link the family above describes g(f(b)) and the natural-scale prediction is g^{-1} of the fitted curve.

When predict_type = "se" the learner reports two link-scale standard errors: se_epistemic, the Gauss-Newton delta-method SD of the mean curve (parameter covariance \(\hat\sigma^2 (H/2)^{-1}\) propagated through the gradient of f), and se, the total predictive SD sqrt(se_epistemic^2 + sigma2) that adds the residual variance back. If the Hessian is singular or the residual degrees of freedom are non-positive, both are NA. Predictive quantiles (predict_type = "quantiles") are the exact Normal quantiles of that predictive, back-transformed to the natural scale.

Multiple archive rows belonging to the same batch are collapsed via the batch-wise mean of target before fitting; ties always agree by construction when the upstream task was produced by CallbackSurrogatePerformance.

Creates a new instance of this learner.

Parameters

• asymptote_init, amplitude_init, rate_init :: numeric(1)
  Initial values for c, a, and k. Defaults derived from the training data when unset.

• rate_lower :: numeric(1)
  Lower bound for the decay rate k. Initialized to 1e-6 so the curve stays monotone and the model identifiable.

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