In　this　paper,　we　introduce　a　variety　of　acquisition　functions　currently　used　in　Bayesian　optimization.　Besides　the　traditional　acquisition　functions　like　Probability　Improvement　(PI),　Expected　Improvement　(EI)　and　Gaussian　Process-Upper　Confidence　Bound　(GP-UCB),　we　also　present　some　modified　or　improved　EI　and　PI　methods,　Knowledge　Gradient　(KG)　and　Predictive　Entropy　Search　(PES)　methods　to　explore　ways　to　reduce　the　impact　of　observational　noise.　In　experimental　part,　we　choose　a　benchmark　function　and　use　Bayesian　optimization　algorithm　to　find　its　global　minimum.　We　add　different　scales　of　noise　in　particular　following　the　Gaussian　distribution　to　the　benchmark　function,　to　compare　the　performance　of　BO　algorithm　using　different　acquisition　functions.　Combined　with　the　experimental　results,　we　also　present　a　discussion　of　the　pros　and　cons　of　using　those　acquisition　functions.　Hope　this　can　provide　some　experience　and　suggestions　for　choosing　acquisition　functions　in　terms　of　noisy　observation.