进化策略的质心几何解释
Center-of-Mass Interpretation of Evolution Strategies
AI 导读
一篇 arXiv 论文为进化策略（ES）的参数更新提出几何解释：把每个受扰动的模型视为粒子、奖励视为质量，群体会平衡在奖励加权的质心处。论文证明去均值的 ES 更新恰好等于这一位移乘以与平均奖励相关的标量因子，对任意有限种群都精确成立；在大种群或对偶采样下，模型从当前位置向自身种群的奖励加权质心移动。
正文 · 原文
Abstract:Evolution strategies (ES) update a model by sampling a population of perturbed copies, scoring each one, and moving in the reward-weighted direction of the perturbations. This update is usually presented as an estimate of a smoothed gradient. We present a geometrical interpretation of this update instead. Treat each perturbed model as a particle and its reward as the particle's mass. Before scoring, every particle has the same mass and the population balances at its centroid. Once rewards are assigned, it balances at its reward-weighted center of mass instead. We show that the mean-subtracted ES update is exactly this displacement, scaled by a scalar factor that depends on the mean reward, for any finite population. The physical reading needs nonnegative rewards, which can always be arranged by adding a constant to every reward without changing the update. In the limit of a large population or under antithetic sampling, the centroid sits on the model itself, so ES has an even simpler geometric interpretation: from its current location, the model moves towards the reward-weighted center of mass of its own population. The same picture explains what subtracting the mean reward does: it changes the point from which the displacement is measured, from the model to the sampled centroid. Our contribution is an intuitive, geometric way to visualize an ES update, exact for any finite population.
| Subjects: | Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2610.35865 [cs.AI] |
| (or arXiv:2610.35865v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.35865 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Akshat Gupta [view email]
[v1]
Mon, 26 Oct 2026 17:59:33 UTC (180 KB)
来源：arXiv cs.AI · arxiv.org