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Stability Conditions for Online Learnability [article]
2011 arXiv pre-print
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We introduce online stability, a stability condition related to uniform-leave-one-out stability in the batch setting, that is sufficient for online learnability. ... We provide examples that suggest the existence of an algorithm with such stability condition might in fact be necessary for online learnability. ... While we haven't been able to provide necessary conditions for online learnability in the general learning setting, we have shown that all problems with a sub-exponential covering are all online learnable ...
arXiv:1108.3154v2 fatcat:txcs3ssgurclboyjdpt42grvgi
On the Equivalence between Online and Private Learnability beyond Binary Classification [article]
2021 arXiv pre-print
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While the equivalence for regression remains open, we provide non-trivial sufficient conditions for an online learnable class to also be privately learnable. ... First, we show that private learnability implies online learnability in both settings. ... Instead, we provide sufficient conditions for private learnability in regression problems. Theorem 15 (Sufficient conditions for private regression learnability). ...
arXiv:2006.01980v3 fatcat:2evrzmik5jgnba4yy7xy2pj3ea
The Interplay Between Stability and Regret in Online Learning [article]
2012 arXiv pre-print
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This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). ... Our stability-regret connection provides a simple recipe for analyzing regret incurred by any online learning algorithm. ... Three conditions for online learning In this section, we formally define our stability notion as well as introduce our bounded forward regret condition. ...
arXiv:1211.6158v1 fatcat:vhxhmseqajdbbmpfqw2vx3svf4
Stochastic Convex Optimization
2009 Annual Conference Computational Learning Theory
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for meaningful non-trivial learnability. ... For supervised classification problems, it is well known that learnability is equivalent to uniform convergence of the empirical risks and thus to learnability by empirical minimization. ... Acknowledgments We would like to thank Leon Bottou, Tong Zhang, and Vladimir Vapnik for helpful discussions. ...
dblp:conf/colt/Shalev-ShwartzSSS09 fatcat:5o2nz6pspjhcdch4uw6kc7wtpi
Learning From An Optimization Viewpoint [article]
2012 arXiv pre-print
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To fill this void we use stability of learning algorithms to fully characterize statistical learnability in the general setting. Next we consider the problem of online learning. ... We further use these tools to fully characterize learnability for online supervised learning problems. II. ... That means finding some condition which is both necessary and sufficient for learnability. ...
arXiv:1204.4145v1 fatcat:etcvc6ilvrdzdg5caanvogtp5a
MODEL THEORY AND MACHINE LEARNING
2019 Bulletin of Symbolic Logic
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In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online ... In particular, this gives many new examples of mathematically interesting classes which are learnable in the online setting. ... The correspondence between online learnability and stability is similar to the correspondence between PAC-learnability and NIP, but it should be mentioned that the fields (online learning and stability ...
doi:10.1017/bsl.2018.71 fatcat:plwknoxqjjhpbh367uz7m6vro4
Online learnability of Statistical Relational Learning in anomaly detection [article]
2017 arXiv pre-print
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Operational requirements for online learning stability are outlined and compared to mathematical definitions as applied to the learning process of a representative SRL method - Bayesian Logic Programs ... It is found that learning algorithms in initial stages of online learning can lock on unstable false predictors that nevertheless comply with our tentative stability requirements and thus masquerade as ... Formal stability conditions for online learning Ross and Bagnell [13] provide an up-to-date review on what is known about stability conditions for online learnability in the context of the General Setting ...
arXiv:1705.06573v1 fatcat:ialfz64fcvh6lkdnb55f5ifyl4
An Equivalence Between Private Classification and Online Prediction [article]
2021 arXiv pre-print
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Together these two results yield an equivalence between online learnability and private PAC learnability. ... We introduce a new notion of algorithmic stability called "global stability" which is essential to our proof and may be of independent interest. ... We also thank Yuval Dagan for providing useful comments and for insightful conversations. ...
arXiv:2003.00563v3 fatcat:xxr6uppdevfk7e7pesxlvglkje
Private and Online Learnability are Equivalent
2022 Journal of the ACM
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This implies a qualitative equivalence between online learnability and private PAC learnability. ... We also thank Raef Bassily and Yuval Dagan for providing useful comments and for insightful conversations. ... ACKNOWLEDGEMENTS We would like to thank Amos Beimel and Uri Stemmer for pointing out and helping to ix a mistake in the derivation of Corollary 4 in a previous version. ...
doi:10.1145/3526074 fatcat:vr3vtpgtd5bp3ibfg37jox55fu
Intrinsic fluctuations of reinforcement learning promote cooperation [article]
2022 arXiv pre-print
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While evolutionary theory revealed a range of mechanisms promoting cooperation, the conditions under which agents learn to cooperate are contested. ... Each of the two learning agents learns a strategy that conditions the following action choices on both agents' action choices of the last round. ... Acknowledgements This work was supported by the German Federal Ministry of Education and Research (BMBF): Tuebingen AI Center, FKZ: 01IS18039A, and the Dutch Institute for Emergent Phenomena (DIEP) cluster ...
arXiv:2209.01013v1 fatcat:rln5kig32vgfpjiy4yjutom3xq
Online learning with dynamics: A minimax perspective [article]
2020 arXiv pre-print
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Our main results provide sufficient conditions for online learnability for this setup with corresponding rates. ... Our approach provides a unifying analysis that recovers regret bounds for several well studied problems including online learning with memory, online control of linear quadratic regulators, online Markov ... Acknowledgments We would like to thank Dylan Foster, Mehryar Mohri and Ayush Sekhari for helpful discussions. KB is supported by a JP Morgan AI Fellowship. ...
arXiv:2012.01705v1 fatcat:bhhidmzdazftnnl53u2jssxmgq
The unstable formula theorem revisited [article]
2022 arXiv pre-print
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We first prove that Littlestone classes, those which model theorists call stable, characterize learnability in a new statistical model: a learner in this new setting outputs the same hypothesis, up to ... This fills a certain gap in the literature, and sets the stage for an approximation theorem characterizing Littlestone classes in terms of a range of learning models, by analogy to definability of types ... H has online -approximations in the sense of Definition 7.2. A3. H is online learnable. B. Combinatorial parameters B1. (X, H) has finite half-graphs. B2. (X, H) has finite Littlestone dimension. B3. ...
arXiv:2212.05050v1 fatcat:e773b6bl5fbrhmu4hklqmkl4ma
Undecidability of Learnability [article]
2021 arXiv pre-print
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For PAC binary classification, uniform and universal online learning, and exact learning through teacher-learner interactions, learnability is in general undecidable, both in the sense of independence ... learnability. ... Wolf for stimulating discussions on questions of (un-)decidability and for suggesting the reasoning used in Subsection 3.2. ...
arXiv:2106.01382v2 fatcat:bawoexdvwfcmdblveyxizasrym
The Bayesian Stability Zoo [article]
2023 arXiv pre-print
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, TV stability, mutual information stability, KL-divergence stability, and R\'enyi-divergence stability. ... We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian stability. ... Neither the European Union nor the granting authority can be held responsible for them. ...
arXiv:2310.18428v2 fatcat:dfudy2ei3fce5kptcrvnnzkohy
On the Hardness of PAC-learning Stabilizer States with Noise [article]
2022 arXiv pre-print
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We consider the problem of learning stabilizer states with noise in the Probably Approximately Correct (PAC) framework of Aaronson (2007) for learning quantum states. ... We prove an exponential lower bound on learning stabilizer states in the SQ model. ... Acknowledgements We thank Scott Aaronson, Srinivasan Arunachalam, and Andrea Rocchetto for many helpful discussions. ...
arXiv:2102.05174v3 fatcat:sl73w5s4sfgpvenwz2f7jrngfq
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