标题： 关于汤普森采样和加性贝叶斯优化中的双边不确定性 显示英文标题

标题： On Thompson Sampling and Bilateral Uncertainty in Additive Bayesian Optimization

摘要： 在贝叶斯优化（BO）中，加法假设可以缓解在高维空间中建模和搜索复杂函数的双重困难。 然而，常见的获取函数，如加法下限置信区间，忽略了维度之间的成对协方差，我们将这称为\textit{双边不确定性} （BU），这引入了第二层近似。 虽然理论结果表明这样做在渐近意义上损失不大，但关于这种假设在小预算下的实际影响知之甚少。 在本文中，我们表明通过利用条件独立性，可以高效地进行尊重 BU 的汤普森采样。 我们利用这一事实对忽略 BU 所造成的损失进行了实证研究，发现从整体上看，对汤普森采样的加法近似确实比精确方法表现更差，但这种差异在实践中意义不大。 这加强了理论理解，并表明在实践中，即使在非渐近情况下，忽略 BU 的近似方法对于 BO 也是足够的。 显示英文摘要

摘要： 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.