One of the most critical problems in machine learning is HyperParameter Optimization (HPO), since choice of hyperparameters has a significant impact on final model performance. Although there are many HPO algorithms, they either have no theoretical guarantees or require strong assumptions. To this end, we introduce BLiE -- a Lipschitz-bandit-based algorithm for HPO that only assumes Lipschitz continuity of the objective function. BLiE exploits the landscape of the objective function to adaptively search over the hyperparameter space. Theoretically, we show that $(i)$ BLiE finds an $\epsilon$-optimal hyperparameter with $\mathcal{O} \left( \epsilon^{-(d_z + \beta)}\right)$ total budgets, where $d_z$ and $\beta$ are problem intrinsic; $(ii)$ BLiE is highly parallelizable. Empirically, we demonstrate that BLiE outperforms the state-of-the-art HPO algorithms on benchmark tasks. We also apply BLiE to search for noise schedule of diffusion models. Comparison with the default schedule shows that BLiE schedule greatly improves the sampling speed.

翻译：机器学习中最关键的问题之一是超参数优化（HPO），因为超参数的选择会对最终模型性能产生显著影响。尽管存在许多HPO算法，但它们要么缺乏理论保证，要么需要强假设条件。为此，我们提出BLiE——一种基于Lipschitz bandit的HPO算法，该算法仅假设目标函数满足Lipschitz连续性。BLiE利用目标函数的景观特征在超参数空间中进行自适应搜索。理论方面，我们证明：(i) BLiE在总预算为$\mathcal{O} \left( \epsilon^{-(d_z + \beta)}\right)$的条件下能够找到$\epsilon$-最优超参数，其中$d_z$和$\beta$是问题固有的参数；(ii) BLiE具有高度可并行性。实验方面，我们证明BLiE在基准任务上优于最先进的HPO算法。我们还将BLiE应用于扩散模型噪声调度的搜索，与默认调度相比，BLiE调度显著提升了采样速度。