改进贝叶斯优化中忽略维度间相关性的方法，实证表明影响微乎其微。
On Thompson Sampling and Bilateral Uncertainty in Additive Bayesian Optimization
- 利用条件独立性设计保留双边不确定性的汤普森采样算法
- 在小预算下对比发现忽略双边不确定性性能略差但差别不大
- 适合关注高维优化中近似合理性与实际效果的研究者
在贝叶斯优化（BO）中，加性假设可缓解高维复杂函数建模与搜索的双重困难。然而，常见采集函数（如加性低置信界）忽略了维度间的成对协方差，即所谓‘双边不确定性’（BU），引入了第二层近似。尽管理论表明渐近下损失不大，但小预算下的实际影响尚不明确。本文证明通过条件独立性可高效实现尊重BU的汤普森采样。基于此开展实证研究，发现忽略BU的加性近似虽整体性能略逊于精确方法，但差异在实践中可忽略。这支持了既有理论，并表明在非渐近场景下，忽略双边不确定性的近似仍足够有效。
原文摘要 · Abstract (English)
In Bayesian Optimization (BO), additive assumptions can mitigate the twin difficulties of modeling and searching a complex function in high dimension. However, common acquisition functions, like the Additive Lower Confidence Bound, ignore pairwise covariances between dimensions, which we'll call \textit{bilateral uncertainty} (BU), imposing a second layer of approximations. While theoretical results indicate that asymptotically not much is lost in doing so, little is known about the practical effects of this assumption in small budgets. In this article, we show that by exploiting conditional independence, Thompson Sampling respecting BU can be efficiently conducted. We use this fact to execute an empirical investigation into the loss incurred by ignoring BU, finding that the additive approximation to Thompson Sampling does indeed have, on balance, worse performance than the exact method, but that this difference is of little practical significance. This buttresses the theoretical understanding and suggests that the BU-ignoring approximation is sufficient for BO in practice, even in the non-asymptotic regime.
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