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1. Teacher Improves Learning by Selecting a Training Subset

   Ma, Yuzhe; Nowak, Robert; Rigollet, Philippe; Zhang, Xuezhou; Zhu, Xiaojin (April 2018, Proceedings of Machine Learning Research)

   We call a learner super-teachable if a teacher can trim down an iid training set while making the learner learn even better. We provide sharp super-teaching guarantees on two learners: the maximum likelihood estimator for the mean of a Gaussian, and the large margin classifier in 1D. For general learners, we provide a mixed-integer nonlinear programming-based algorithm to find a super teaching set. Empirical experiments show that our algorithm is able to find good super-teaching sets for both regression and classification problems. 

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2. Teaching an Active Learner with Contrastive Examples

   Wang, Chaoqi; Singla, Adish; Chen, Yuxin (December 2021, Advances in neural information processing systems)

   We study the problem of active learning with the added twist that the learner is assisted by a helpful teacher. We consider the following natural interaction protocol: At each round, the learner proposes a query asking for the label of an instance xq, the teacher provides the requested label {xq,yq} along with explanatory information to guide the learning process. In this paper, we view this information in the form of an additional contrastive example ({xc,yc}) where xc is picked from a set constrained by xq (e.g., dissimilar instances with the same label). Our focus is to design a teaching algorithm that can provide an informative sequence of contrastive examples to the learner to speed up the learning process. We show that this leads to a challenging sequence optimization problem where the algorithm's choices at a given round depend on the history of interactions. We investigate an efficient teaching algorithm that adaptively picks these contrastive examples. We derive strong performance guarantees for our algorithm based on two problem-dependent parameters and further show that for specific types of active learners (e.g., a generalized binary search learner), the proposed teaching algorithm exhibits strong approximation guarantees. Finally, we illustrate our bounds and demonstrate the effectiveness of our teaching framework via two numerical case studies. 

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3. Learning to find proofs and theorems by learning to refine search strategies

   Laurent, Jonathan; Platzer, André (November 2022, Advances in neural information processing systems)

   Agarwal, Alekh; Belgrave, Danielle; Cho, Kyunghyun; Oh, Alice (Ed.)

   We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to generate tasks of suitable relevance and difficulty for the learner. This allows leveraging minimal amounts of domain knowledge to tackle problems for which training data is unavailable or hard to synthesize. As a specific illustration, we consider loop invariant synthesis for imperative programs and use neural networks to refine both the teacher and solver strategies. 

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4. Orienting to Student Sense-Making: Using Simulations to Support the Development of Equitable Mathematics Teaching

   https://doi.org/10.4018/979-8-3693-1164-6.ch011  

   Shaughnessy, Meghan; Boerst, Timothy A; Garcia, Nicole; Claiborne, Brit (November 2024, IGI Global)

   This chapter reports on work from a decade-long project to develop and study the use of teaching simulations focused on the teaching practices of eliciting and interpreting student thinking to support preservice teachers' (PSTs') learning. The chapter describes how teaching simulations focused on these practices allow teacher educators to support PSTs in orienting to student sense-making that is at the heart of equitable mathematics instruction. The teaching simulation approach is described. Examples illustrate how the approach is designed and facilitated in ways that make visible PSTs' engagement with three teaching performance areas (eliciting the student's process, using mathematical knowledge and skill, and conveying respect for the student as a mathematical thinker and learner) that are crucial for more equitable mathematics instruction. Connections between each of the performance areas and more equitable eliciting and interpreting of student thinking are described alongside the ways in which teacher educators can provide feedback that supports PSTs' development. 

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5. Robust learning under clean-label attack

   Blum, A.; Hanneke, S.; Qian, J.; Shao, H. (January 2021, Conference on Learning Theory)

   Belkin, M.; Kpotufe, S. (Ed.)

   We study the problem of robust learning under clean-label data-poisoning attacks, where the at-tacker injects (an arbitrary set of) correctly-labeled examples to the training set to fool the algorithm into making mistakes on specific test instances at test time. The learning goal is to minimize the attackable rate (the probability mass of attackable test instances), which is more difficult than optimal PAC learning. As we show, any robust algorithm with diminishing attackable rate can achieve the optimal dependence on ε in its PAC sample complexity, i.e., O(1/ε). On the other hand, the attackable rate might be large even for some optimal PAC learners, e.g., SVM for linear classifiers. Furthermore, we show that the class of linear hypotheses is not robustly learnable when the data distribution has zero margin and is robustly learnable in the case of positive margin but requires sample complexity exponential in the dimension. For a general hypothesis class with bounded VC dimension, if the attacker is limited to add at most t >0 poison examples, the optimal robust learning sample complexity grows almost linearly with t. 

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