For bounded real-valued function classes, uniform convergence at scale γ, agnostic learnability at γ/2, and finite fat-shattering dimension above γ are equivalent.
2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) , pages=
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A hypothesis class is learnable in this online precision-recall feedback model if and only if it has finite VC dimension, with algorithms achieving regret bounds in realizable and agnostic settings despite ERM failing.
A dynamic pruning reduction from agnostic to realizable online learning via weak-consistency oracles achieves O(T^{d_VC+1}) query complexity with near-optimal regret and supplies matching upper and lower bounds on the regret-oracle tradeoff.
citing papers explorer
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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale
For bounded real-valued function classes, uniform convergence at scale γ, agnostic learnability at γ/2, and finite fat-shattering dimension above γ are equivalent.
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Online Set Learning from Precision and Recall Feedback
A hypothesis class is learnable in this online precision-recall feedback model if and only if it has finite VC dimension, with algorithms achieving regret bounds in realizable and agnostic settings despite ERM failing.
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Regret-Oracle Complexity Tradeoffs in Agnostic Online Learning
A dynamic pruning reduction from agnostic to realizable online learning via weak-consistency oracles achieves O(T^{d_VC+1}) query complexity with near-optimal regret and supplies matching upper and lower bounds on the regret-oracle tradeoff.