This paper proposes a novel optimization method for hollow-core, anti-resonant fiber based on a gradient descent algorithm assisted via a radial basis-function surrogate model. This approach significantly reduces the number of optimization iterations, achieving a stable improvement in birefringence performance by an order of magnitude across the operating wavelength band. Furthermore, various optimization algorithms were compared, and the indicators of their Pareto sets were analyzed to demonstrate the effectiveness of the proposed method in multi-objective optimization.