# Towards Practical Lipschitz Bandits

## TL;DR

This paper introduces a flexible framework for Lipschitz bandit algorithms that adaptively partitions the space to optimize rewards efficiently, demonstrating state-of-the-art results in real-world tasks like hyperparameter tuning.

## Contribution

We develop a novel adaptive partitioning framework for Lipschitz bandits, linking tree-based methods to Gaussian processes and proposing a hierarchical Bayesian model.

## Key findings

- Achieves state-of-the-art performance in neural network hyperparameter tuning.
- Effectively balances exploration and exploitation through adaptive space partitioning.
- Demonstrates improved regret minimization in real-world applications.

## Abstract

Stochastic Lipschitz bandit algorithms balance exploration and exploitation, and have been used for a variety of important task domains. In this paper, we present a framework for Lipschitz bandit methods that adaptively learns partitions of context- and arm-space. Due to this flexibility, the algorithm is able to efficiently optimize rewards and minimize regret, by focusing on the portions of the space that are most relevant. In our analysis, we link tree-based methods to Gaussian processes. In light of our analysis, we design a novel hierarchical Bayesian model for Lipschitz bandit problems. Our experiments show that our algorithms can achieve state-of-the-art performance in challenging real-world tasks such as neural network hyperparameter tuning.