From 7919c879554182d50bdef8cef7b58c3958815e02 Mon Sep 17 00:00:00 2001 From: Daphne Theodorakopoulos <56087728+daphne12345@users.noreply.github.com> Date: Mon, 13 Jan 2025 14:52:38 +0100 Subject: [PATCH] 1164 docs add source of logei formula (#1188) * Update expected_improvement.py * Added equations and refernces for EI * Added equations and refernces for EI --- smac/acquisition/function/expected_improvement.py | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) diff --git a/smac/acquisition/function/expected_improvement.py b/smac/acquisition/function/expected_improvement.py index db65aa815..b9bbdec8d 100644 --- a/smac/acquisition/function/expected_improvement.py +++ b/smac/acquisition/function/expected_improvement.py @@ -17,11 +17,24 @@ class EI(AbstractAcquisitionFunction): - r"""Expected Improvement (with or without function values in log space) acquisition function + r"""The Expected Improvement (EI) criterion is used to decide where to evaluate a function f(x) next. The goal is to + balance exploration and exploitation. Expected Improvement (with or without function values in log space) + acquisition function :math:`EI(X) := \mathbb{E}\left[ \max\{0, f(\mathbf{X^+}) - f_{t+1}(\mathbf{X}) - \xi \} \right]`, with :math:`f(X^+)` as the best location. + Reference for EI: Jones, D.R. and Schonlau, M. and Welch, W.J. (1998). Efficient Global Optimization of Expensive + Black-Box Functions. Journal of Global Optimization 13, 455–492 + + Reference for logEI: Hutter, F. and Hoos, H. and Leyton-Brown, K. and Murphy, K. (2009). An experimental + investigation of model-based parameter optimisation: SPO and beyond. In: Conference on Genetic and + Evolutionary Computation + + The logEI implemententation is based on the derivation of the orginal equation by: + Watanabe, S. (2024). Derivation of Closed Form of Expected Improvement for Gaussian Process Trained on + Log-Transformed Objective. https://arxiv.org/abs/2411.18095 + Parameters ---------- xi : float, defaults to 0.0