BROS achieves memory-efficient single-loop stochastic bilevel optimization with O(ε^{-2}) sample complexity by performing updates in randomized subspaces and using Rademacher bi-probe correction for unbiased estimation.
Consequently, for anyε < 19 39 2 , the naive projected auxiliary update cannot guaranteeE∥∇Φ(x)∥2 ≤ε even in this noiseless quadratic problem
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BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization
BROS achieves memory-efficient single-loop stochastic bilevel optimization with O(ε^{-2}) sample complexity by performing updates in randomized subspaces and using Rademacher bi-probe correction for unbiased estimation.