More Like this

1. A Distributional-Lifting Theorem for Learning

   Blanc, Guy; Lange, Jane; Strassle, Carmen; Tan, Li-Yang (June 2025, 38th Annual Conference on Learning Theory (COLT 2025))

   The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and relevance. Towards addressing this, we prove a distributional-lifting theorem: This upgrades a learner that succeeds with respect to a limited distribution family \mathcal{D} to one that succeeds with respect to any distribution D^\star, with an efficiency overhead that scales with the complexity of expressing D^\star as a mixture of distributions in \mathcal{D}. Recent work of Blanc, Lange, Malik, and Tan considered the special case of lifting uniform-distribution learners and designed a lifter that uses a conditional sample oracle for D^\star, a strong form of access not afforded by the standard PAC model. Their approach, which draws on ideas from semi-supervised learning, first learns D^\star and then uses this information to lift. We show that their approach is information-theoretically intractable with access only to random examples, thereby giving formal justification for their use of the conditional sample oracle. We then take a different approach that sidesteps the need to learn D^\star, yielding a lifter that works in the standard PAC model and enjoys additional advantages: it works for all base distribution families, preserves the noise tolerance of learners, has better sample complexity, and is simpler. 

   more » « less
2. Efficient, Noise-Tolerant, and Private Learning via Boosting

   Bun, Mark; Carmosino, Marco L.; Sorrell, Jessica (January 2020, Proceedings of Thirty Third Conference on Learning Theory)

   null (Ed.)

   We introduce a simple framework for designing private boosting algorithms. We give natural conditions under which these algorithms are differentially private, efficient, and noise-tolerant PAC learners. To demonstrate our framework, we use it to construct noise-tolerant and private PAC learners for large-margin halfspaces whose sample complexity does not depend on the dimension. We give two sample complexity bounds for our large-margin halfspace learner. One bound is based only on differential privacy, and uses this guarantee as an asset for ensuring generalization. This first bound illustrates a general methodology for obtaining PAC learners from privacy, which may be of independent interest. The second bound uses standard techniques from the theory of large-margin classification (the fat-shattering dimension) to match the best known sample complexity for differentially private learning of large-margin halfspaces, while additionally tolerating random label noise. 

   more » « less
3. 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. 

   more » « less
4. PAC Learnability of Node Functions in Networked Dynamical Systems

   Adiga, Abhijin; Kuhlman, Chris J; Marathe, Madhav V; Ravi, S S; Vulliikanti, Anil (January 2019, Proceedings of the International Conference on Machine Learning)

   null (Ed.)

   We consider the PAC learnability of the functions at the nodes of a discrete networked dynamical system, assuming that the underlying network is known. We provide tight bounds on the sample complexity of learning threshold functions. We establish a computational intractability result for efficient PAC learning of such functions. We develop efficient consistent learners when the number of negative examples is small. Using synthetic and real-world networks, we experimentally study how the network structure and sample complexity influence the quality of inference. 

   more » « less
5. Limitations of Membership Queries in Testable Learning

   Lange, Jane; Qiao, Mingda (January 2026, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026))

   Membership queries (MQ) often yield speedups for learning tasks, particularly in the distribution-specific setting. We show that in the testable learning model of Rubinfeld and Vasilyan [Rubinfeld and Vasilyan, 2023], membership queries cannot decrease the time complexity of testable learning algorithms beyond the complexity of sample-only distribution-specific learning. In the testable learning model, the learner must output a hypothesis whenever the data distribution satisfies a desired property, and if it outputs a hypothesis, the hypothesis must be near-optimal. We give a general reduction from sample-based refutation of boolean concept classes, as presented in [Vadhan, 2017; Kothari and Livni, 2018], to testable learning with queries (TL-Q). This yields lower bounds for TL-Q via the reduction from learning to refutation given in [Kothari and Livni, 2018]. The result is that, relative to a concept class and a distribution family, no m-sample TL-Q algorithm can be super-polynomially more time-efficient than the best m-sample PAC learner. Finally, we define a class of "statistical" MQ algorithms that encompasses many known distribution-specific MQ learners, such as those based on influence estimation or subcube-conditional statistical queries. We show that TL-Q algorithms in this class imply efficient statistical-query refutation and learning algorithms. Thus, combined with known SQ dimension lower bounds, our results imply that these efficient membership query learners cannot be made testable. 

   more » « less