Efficient Bayesian Learning Curve Extrapolation using Prior-Data Fitted
  Networks
Steven Adriaensen Herilalaina Rakotoarison Samuel Müller Frank Hutter
Learning curve extrapolation aims to predict model performance in later
epochs of training, based on the performance in earlier epochs. In this work,
we argue that, while the inherent uncertainty in the extrapolation of learning
curves warrants a Bayesian approach, existing methods are (i) overly
restrictive, and/or (ii) computationally expensive. We describe the first
application of prior-data fitted neural networks (PFNs) in this context. A PFN
is a transformer, pre-trained on data generated from a prior, to perform
approximate Bayesian inference in a single forward pass. We propose LC-PFN, a
PFN trained to extrapolate 10 million artificial right-censored learning curves
generated from a parametric prior proposed in prior art using MCMC. We
demonstrate that LC-PFN can approximate the posterior predictive distribution
more accurately than MCMC, while being over 10 000 times faster. We also show
that the same LC-PFN achieves competitive performance extrapolating a total of
20 000 real learning curves from four learning curve benchmarks (LCBench,
NAS-Bench-201, Taskset, and PD1) that stem from training a wide range of model
architectures (MLPs, CNNs, RNNs, and Transformers) on 53 different datasets
with varying input modalities (tabular, image, text, and protein data).
Finally, we investigate its potential in the context of model selection and
find that a simple LC-PFN based predictive early stopping criterion obtains 2 -
6x speed-ups on 45 of these datasets, at virtually no overhead.