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This paper extends standard results from learning theory with independentdata to sequences of dependent data. Contrary to most of the literature, we donot rely on mixing arguments or sequential measures of complexity and deriveuniform risk bounds with classical proof patterns and capacity measures. Inparticular, we show that the standard classification risk bounds based on theVC-dimension hold in the exact same form for dependent data, and furtherprovide Rademacher complexity-based bounds, that remain unchanged compared tothe standard results for the identically and independently distributed case.Finally, we show how to apply these results in the context of scenario-basedoptimization in order to compute the sample complexity of random programs withdependent constraints.

Uniform Risk Bounds for Learning with Dependent Data Sequences