# A Lipschitz Bandits Approach for Continuous Hyperparameter Optimization

arXiv: https://arxiv.org/abs/2302.01539 · HTML: https://mlsanity.com/paper/2302.01539/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 70 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Non-stochastic Best Arm Identification and Hyperparameter Optimization](https://mlsanity.com/paper/1502.07943/) (2015)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Batched Multi-armed Bandits Problem](https://mlsanity.com/paper/1904.01763/) (2019)
- [Provably Efficient Online Hyperparameter Optimization with Population-Based Bandits](https://mlsanity.com/paper/2002.02518/) (2020)
- [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020)
- [Sequential Batch Learning in Finite-Action Linear Contextual Bandits](https://mlsanity.com/paper/2004.06321/) (2020)
- [Online Learning with Switching Costs and Other Adaptive Adversaries](https://mlsanity.com/paper/1302.4387/) (2013)
- [Lipschitz Bandits: Regret Lower Bounds and Optimal Algorithms](https://mlsanity.com/paper/1405.4758/) (2014)
- [Gaussian Process Bandit Optimization with Few Batches](https://mlsanity.com/paper/2110.07788/) (2021)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Linear Bandits with Limited Adaptivity and Learning Distributional Optimal Design](https://mlsanity.com/paper/2007.01980/) (2020)
- [Regret Bounds for Batched Bandits](https://mlsanity.com/paper/1910.04959/) (2019)
- [Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting](https://mlsanity.com/paper/1902.01520/) (2019)
- [Collaborative Learning with Limited Interaction: Tight Bounds for Distributed Exploration in Multi-Armed Bandits](https://mlsanity.com/paper/1904.03293/) (2019)
- [Simple regret for infinitely many armed bandits](https://mlsanity.com/paper/1505.04627/) (2015)

## Built on by (most cited first, 9 of 9)

- [One-Step Diffusion Distillation through Score Implicit Matching](https://mlsanity.com/paper/2410.16794/) (2024)
- [Diff-Instruct++: Training One-step Text-to-image Generator Model to Align with Human Preferences](https://mlsanity.com/paper/2410.18881/) (2024)
- [Flow Generator Matching](https://mlsanity.com/paper/2410.19310/) (2024)
- [David and Goliath: Small One-step Model Beats Large Diffusion with Score Post-training](https://mlsanity.com/paper/2410.20898/) (2024)
- [Quantum Lipschitz Bandits](https://mlsanity.com/paper/2504.02251/) (2025)
- [Narrowing Action Choices with AI Improves Human Sequential Decisions](https://mlsanity.com/paper/2510.16097/) (2025)
- [From Random Search to Bandit Learning in Metric Measure Spaces](https://mlsanity.com/paper/2305.11509/) (2023)
- [Learning Rate Optimization for Deep Neural Networks Using Lipschitz Bandits](https://mlsanity.com/paper/2409.09783/) (2024)
- [Instance-dependent Stochastic Lipschitz bandit](https://mlsanity.com/paper/2605.29748/) (2026)

## Abstract (arXiv)

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 ε-optimal hyperparameter with O left( ε-(dz + β)right) total budgets, where dz and β 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.