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I'm dealing with a regression prediction challenge where the evaluation metric is (pearson) correlation. However, I have the impression that this metric is kind of arbitrary. While I can keep the RMSE stable the correlation can have great variety.

Could someone please explain this metric and how to optimise for it?

I'm slightly confused; if you don't think this is an appropriate metric, why are you using it? – Emre – 2016-01-24T06:37:42.213

@Emre because the challenge organizers defined it to be their evaluation metric – spore234 – 2016-01-24T09:40:34.477