The explosive growth of data and its related energy consumption is pushing the need to develop energy-efficient brain-inspired schemes and materials for data processing and storage. Here, we demonstrate experimentally that Co/Pt films can be used as artificial synapses by manipulating their magnetization state using circularly-polarized ultrashort optical pulses at room temperature. We also show an efficient implementation of supervised perceptron learning on an opto-magnetic neural network, built from such magnetic synapses. Importantly, we demonstrate that the optimization of synaptic weights can be achieved using a global feedback mechanism, such that the learning does not rely on external storage or additional optimization schemes. These results suggest there is high potential for realizing artificial neural networks using optically-controlled magnetization in technologically relevant materials, that can learn not only fast but also energy-efficient.