含噪声损失测量的盲随机搜索：平均、阈值化与几乎必然收敛
Blind Random Search with Noisy Loss Measurements: Averaging, Thresholding, and Almost Sure Convergence
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中文总结 AI 辅助
该研究针对含噪声损失测量的盲随机搜索问题，通过结合平均与阈值化技术，实现了真实损失的几乎必然收敛。
中文摘要 AI 辅助
盲随机搜索会反复抽取候选点，若候选点的损失更低则替换当前估计值。在无噪声时，可直接观测到真实损失，其在每次接受的更新中严格递减，且在所有迭代中呈非递增趋势。测量噪声可能使更差的候选点表现得更好，从而打破该单调性。为在噪声下恢复几乎必然收敛，我们在原决策准则中结合了平均与阈值化这两种经典工具，二者相互耦合；随着样本量增大，正阈值会以匹配的速率缩小。这些修改使盲随机搜索在含噪声测量下恢复了真实损失的最终单调性，并实现几乎必然收敛。
英文摘要
Blind random search repeatedly draws a candidate point and replaces the current estimate whenever the candidate has a lower loss. In the absence of noise, the true loss is observed directly. It decreases strictly at every accepted update and is monotone nonincreasing over all iterations. Measurement noise can make a worse candidate appear better and thereby break this monotonicity. To recover almost sure convergence under noise, we incorporate averaging and thresholding into the original decision criterion. These two classical tools are coupled. As the sample sizes grow, the positive threshold shrinks at a matched rate. These modifications allow blind random search to recover eventual monotonicity of the true loss under noisy measurements and to converge almost surely.
