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This paper presents a new logarithmic-free upper bound for the generalization gap in uniformly stable algorithms and constructs a deterministic learning problem that achieves optimal high-probability dependence, closing a gap in the literature.
This paper provides optimal high-probability bounds for stochastic gradient descent under Markovian noise for PL-smooth objectives, closing gaps between expectation and high-probability guarantees and extending to heavy-tailed settings with matching lower bounds.