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The number of Internet of Things devices generating data streams is expected to grow exponentially with the support of emergent technologies such as 5G networks. Therefore, the online processing of these data streams requires the design and development of suitable machine learning algorithms, able to learn online, as data is generated. Like their batch-learning counterparts, stream-based learning algorithms require careful hyperparameter settings. However, this problem is exacerbated in online learning settings, especially with the occurrence of concept drifts, which frequently require the reconfiguration of hyperparameters. In this article, we present SSPT, an extension of the Self Parameter Tuning (SPT) optimisation algorithm for data streams. We apply the Nelder–Mead algorithm to dynamically-sized samples, converging to optimal settings in a single pass over data while using a relatively small number of hyperparameter configurations. In addition, our proposal automatically readjusts hyperparameters when concept drift occurs. To assess the effectiveness of SSPT, the algorithm is evaluated with three different machine learning problems: recommendation, regression, and classification. Experiments with well-known data sets show that the proposed algorithm can outperform previous hyperparameter tuning efforts by human experts. Results also show that SSPT converges significantly faster and presents at least similar accuracy when compared with the previous double-pass version of the SPT algorithm.