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This paper proves lower bounds for smooth nonconvex zeroth-order optimization, showing that deterministic methods incur an extra factor of roughly d in query complexity compared to randomized methods under low curvature trace conditions, quantifying the price of determinism for tasks like LLM fine-tuning with function-value-only queries.
This paper introduces a new instance-optimal protocol for AI debate in scalable oversight that guarantees worst-case correctness, makes honesty a dominant-strategy equilibrium, and proves black-box lower bounds showing no protocol can outperform it on problems with stable decompositions.