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.
Robust stochastic approx- imation approach to stochastic programming.SIAM Journal on optimization, 19(4):1574–1609
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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.