The objective of the proposed research is to develop methods for effective knowledge transmission from expert teachers to learning algorithms. First, we expand the framework of online machine teaching by accounting for uncertainty in the learner's initial state and unknown alignments between teacher and learner latent spaces. We focus on learners performing gradient descent of a quadratic loss and propose an algorithm in which the teacher simultaneously infers the state of the learner while guiding its learning. Next, we address scenarios in which learning algorithms learn from humans. Traditional methods often reduce human feedback to binary labels, requiring numerous interactions. To improve efficiency, we design and analyze richer forms of feedback. Lastly, we focus on interactive graph search. We propose a strategy to find a target node, with informative queries in the presence of oracle noise. The proposed work advances knowledge transmission in machine learning by accounting for learner uncertainty, leveraging nuanced human feedback, and optimizing hierarchical search.