Abstract: A federated learning system in which a plurality of local servers repeatedly learn cooperatively through communications between the plurality of local servers and a central server via a network. The local server includes a decryption unit, a mean gradient calculation unit, a model updating unit, a validation error calculation unit, an encryption unit, and a local transmission unit that transmits at least one of a current local mean gradient and a current local validation error. The central server includes a central reception unit, a model selection unit, a weight determination unit, and a central transmission unit. The central reception unit receives encrypted current local models and at least one of current local training data counts, the current local mean gradients, and the current local validation errors from the plurality of respective local servers.