Domain Generalization (DG) research has gained considerable traction as of late,since the ability to generalize to unseen data distributions is a requirementthat eludes even state-of-the-art training algorithms. In this paper we observethat the initial iterations of model training play a key role in domaingeneralization effectiveness, since the loss landscape may be significantlydifferent across the training and test distributions, contrary to the case ofi.i.d. data. Conflicts between gradients of the loss components of each domainlead the optimization procedure to undesirable local minima that do not capturethe domain-invariant features of the target classes. We propose alleviatingdomain conflicts in model optimization, by iteratively annealing the parametersof a model in the early stages of training and searching for points wheregradients align between domains. By discovering a set of parameter values where gradientsare updated towards the same direction for each data distribution present in thetraining set, the proposed Gradient-Guided Annealing (GGA) algorithm encouragesmodels to seek out minima that exhibit improved robustness against domainshifts. The efficacy of GGA is evaluated on four widely accepted and challengingimage classification domain generalization benchmarks, where its use alone isable to establish highly competitive or even state-of-the-art performance.Moreover, when combined with previously proposed domain-generalizationalgorithms it is able to consistently improve their effectiveness by significantmargins.