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Autonomous agents interacting with the real world need to learn new concepts efficiently and reliably. This requires learning in a low-data regime, which is a highly challenging problem. We address this task by introducing a fast optimization-based meta-learning method for few-shot classification. It consists of an embedding network, providing a general representation of the image, and a base learner module. The latter learns a linear classifier during the inference through an unrolled optimization procedure. We design an inner learning objective composed of (i) a robust classification loss on the support set and (ii) an entropy loss, allowing transductive learning from unlabeled query samples. By employing an efficient initialization module and a Steepest Descent based optimization algorithm, our base learner predicts a powerful classifier within only a few iterations. Further, our strategy enables important aspects of the base learner objective to be learned during meta-training. To the best of our knowledge, this work is the first to integrate both induction and transduction into the base learner in an optimization-based meta-learning framework. We perform a comprehensive experimental analysis, demonstrating the speed and effectiveness of our approach on four few-shot classification datasets. The Code is available at \href{https://github.com/4rdhendu/FIML}{\textcolor{blue}{https://github.com/4rdhendu/FIML}}.