Sample-Conditioned Hypothesis Stability Sharpens Information-Theoretic Generalization Bounds
This work addresses limitations in generalization theory for machine learning practitioners, though it appears incremental as it builds on existing information-theoretic frameworks.
The paper tackles the problem of deriving sharper information-theoretic generalization bounds by introducing sample-conditioned hypothesis stability, improving upon previous bounds in scenarios like stochastic convex optimization.
We present new information-theoretic generalization guarantees through the a novel construction of the "neighboring-hypothesis" matrix and a new family of stability notions termed sample-conditioned hypothesis (SCH) stability. Our approach yields sharper bounds that improve upon previous information-theoretic bounds in various learning scenarios. Notably, these bounds address the limitations of existing information-theoretic bounds in the context of stochastic convex optimization (SCO) problems, as explored in the recent work by Haghifam et al. (2023).