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This paper addresses the trade-off between frequency control performance and cost in islanded microgrids, where higher performance requires higher cost. We propose a data-driven frequency control (DDS-FC) method that treats the microgrid frequency controller as an intelligent agent that can learn and decide autonomously how to balance the power output and control performance of each unit. To implement this method, we develop a Priority experience replay soft deep actor critic (PER-SAC) algorithm, which improves upon traditional deep reinforcement learning algorithms by using maximum entropy exploration to obtain more diverse and informative samples, thereby enhancing the algorithm’s robustness, convergence, and quality. It validates the proposed method on the microgrid model of the Southern Power Grid and show that it effectively exploits the frequency regulation potential of distributed power sources and energy storage, resulting in lower frequency deviation and generation cost.