Sample-Conditioned Hypothesis Stability Sharpens Information-Theoretic
  Generalization Bounds
Ziqiao Wang Yongyi Mao
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).