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We describe ASAGA, an asynchronous parallel version of the incremental gradient algorithm SAGA that enjoys fast linear convergence rates. Through a novel perspective, we revisit and clarify a subtle but important technical issue present in a large fraction of the recent convergence rate proofs for asynchronous parallel optimization algorithms, and propose a simplification of the recently introduced “perturbed iterate” framework that resolves it. We thereby prove that ASAGA can obtain a theoretical linear speedup on multi-core systems even without sparsity assumptions. We present results of an implementation on a 40-core architecture illustrating the practical speedup as well as the hardware overhead.