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Heavy-Tailed First-Order Optimization for Polyak-Łojasiewicz Condition: High-Dimensional Minimax Bounds, High-Probability Guarantee, and Fixed-Dimensional Improvements
We study smooth Polyak--Łojasiewicz (PL) optimization with conditionally unbiased stochastic gradients satisfying \[ \mathbb E\!\left[ \|G_t-\nabla f(x_t)\|^α\mid\mathcal F_{t-1} \right]\le σ^α, \qquad 1<α\le2. \] When the dimension may depend on the oracle budget, we prove the noise-adaptive lower
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