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This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical norm. This result is convenient to apply in real applications and could yield refined local Rademacher complexity bounds for function classes satisfying general entropy conditions. We demonstrate the power of our complexity bounds by applying them to derive effective generalization error bounds.
This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance by (local)
We study covering numbers and local covering numbers with respect to difference graphs and complete bipartite graphs. In particular we show that in every cover of a Young diagram with $binom{2k}{k}$ steps with generalized rectangles there is a row or
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric inequalities on cover
Fairness in algorithmic decision-making processes is attracting increasing concern. When an algorithm is applied to human-related decision-making an estimator solely optimizing its predictive power can learn biases on the existing data, which motivat
The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs cl