Stochastic optimization algorithms are widely employed for problems arising in machine learning but significant issues in their use are open. In fact, tuning these algorithms for each application may require an extremely high computational cost. Research for Green Artificial Intelligence aims to make efficiency an evaluation criterion along with accuracy. Adaptive optimization algorithms, borrowed from deterministic optimization and based on probabilistic models, are currently investigated as an alternative to avoid expensive tuning. In this talk we discuss these issues and present a first-order trust-region method where the models and the stepsize selection are adjusted dynamically along the iterations via the inexact restoration method and the trust-region machinery.