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Surrogate models are widely applied in many scenarios to replace expensive executions of real-world procedures. Training a high-quality surrogate model often requires many sample points, which can be costly to obtain. We would amortize this cost if we could reuse already-trained surrogates in future tasks, provided certain invariances are retained across tasks. This paper studies transferring a surrogate model trained on a source function to a target function using a small data set. As a first step, we consider the following invariance: the domains of the source and target functions are related by an unknown affine transformation. We propose to parameterize the surrogate of the source with an affine transformation and optimize it w.r.t. an empirical loss measured with a small transfer data set sampled on the target. We select all functions from the well-known black-box optimization benchmark (BBOB) as the source …