We present a new synthesis algorithm to solve program synthesis over noisy datasets, i.e., data that may contain incorrect/corrupted input-output examples. Our algorithm uses an abstraction refinement based optimization process to synthesize programs which optimize the tradeoff between the loss over the noisy dataset and the complexity of the synthesized program. The algorithm uses abstractions to divide the search space of programs into subspaces by computing an abstract value that represents outputs for all programs in a subspace. The abstract value allows our algorithm to compute, for each subspace, a sound approximate lower bound of the loss over all programs in the subspace. It iteratively refines these abstractions to further subdivide the space into smaller subspaces, prune subspaces that do not contain an optimal program, and eventually synthesize an optimal program. We implemented this algorithm in a tool called Rose. We compare Rose to a current state-of-the-art noisy program synthesis system using the SyGuS 2018 benchmark suite. Our evaluation demonstrates that Rose significantly outperforms this previous system: on two noisy benchmark program synthesis problems sets drawn from the SyGus 2018 benchmark suite, Rose delivers speedups of up to 1587 and 81.7, with median speedups of 20.5 and 81.7. Rose also terminates on 20 (out of 54) and 4 (out of 11) more benchmark problems than the previous system. Both Rose and the previous system synthesize programs that are optimal over the provided noisy data sets. For the majority of the problems in the benchmark sets ($272$ out of $286$), the synthesized programs also produce correct outputs for all inputs in the original (unseen) noise-free data set. These results highlight the benefits that Rose can deliver for effective noisy program synthesis.