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

@@ -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