The complexity of stochastic continuous simulation optimization is the maximum of variance-dependent and variance-independent terms, so low-noise finite-budget cases match deterministic complexity until the budget grows large enough for noise to dominate.
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Understanding the Variance Dichotomy in Continuous Simulation Optimization: A Minimax Lower Bound Perspective
The complexity of stochastic continuous simulation optimization is the maximum of variance-dependent and variance-independent terms, so low-noise finite-budget cases match deterministic complexity until the budget grows large enough for noise to dominate.