通过裁剪模型输出，让自适应优化在不确定条件下仍高效收敛。
Clipping the Price of Adaptivity at the Tail
- 在模型-损失分解结构下，对异常输出进行尾部裁剪。
- 在距离与光滑性不确定性大的情况下，达到最优率的对数级近似。
- 适合需鲁棒自适应优化的机器学习任务，如强化学习、在线学习。
自适应随机凸优化方法面临一个根本性的‘自适应代价’障碍：在标准假设下，无法有效适应初始距离与Lipschitz常数中的大不确定性。我们通过引入许多学习问题中共有的额外结构来规避这一障碍。具体而言，假设目标函数可分解为模型与损失函数，允许我们在损失函数前干预模型输出。在此假设下，设计了一种方法，在尾部事件中对偏离固定参考模型过远的输出进行裁剪。该方法在已知参数的随机凸优化最优界上，仅相差对数因子，从而在距离和Lipschitz参数的不确定性均较大时仍能高效自适应。
原文摘要 · Abstract (English)
Adaptive stochastic convex optimization (SCO) methods face a fundamental ``price of adaptivity'' barrier: under the standard set of assumptions, they cannot efficiently adapt to large uncertainty in both the initial distance to optimality and the Lipschitz constant. We circumvent this barrier by requiring a small amount of additional structure common to many learning problems. Specifically, we assume that the objective decomposes into a model and a loss function, enabling us to intervene by modifying the model's output before it passes to the loss function. Under this assumption, we design a method that clips the learned model output in tail events where it deviates too much from the output of a fixed reference model. Our method matches the optimal bounds for known-parameter SCO up to logarithmic factors in the uncertainty in the distance and Lipschitz parameters, thus efficiently adapting to large uncertainty in both.
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