Partial-label learning is one of the important weakly supervised learning problems, where each training example is equipped with a set of candidate labels that contains the true label. Most existing methods elaborately designed learning objectives as constrained optimizations that must be solved in specific manners, making their computational complexity a bottleneck for scaling up to big data. The goal of this paper is to propose a novel framework of partial-label learning without implicit assumptions on the model or optimization algorithm. More specifically, we propose a general estimator of the classification risk, theoretically analyze the classifier-consistency, and establish an estimation error bound. We then explore a progressive identification method for approximately minimizing the proposed risk estimator, where the update of the model and identification of true labels can be conducted in a seamless manner. The resulting algorithm is model-independent and loss-independent, and compatible with stochastic optimization. Thorough experiments demonstrate it sets the new state of the art.