For φ-divergences with superlinear growth, sample average approximation achieves P-independent sample complexity for worst-case expectation estimation depending only on φ's growth, ball radius and precision, with optimality via lower bounds; non-superlinear φ yields unbounded P-dependent complexity.
Sample complexity of variance-reduced distributionally robust q-learning.Journal of Machine Learning Research, 25(341):1–77
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Sample Average Approximation for Distributionally Robust Optimization with $\phi$-divergences
For φ-divergences with superlinear growth, sample average approximation achieves P-independent sample complexity for worst-case expectation estimation depending only on φ's growth, ball radius and precision, with optimality via lower bounds; non-superlinear φ yields unbounded P-dependent complexity.