# Optimization for Gaussian Processes via Chaining

arXiv: https://arxiv.org/abs/1510.05576 · HTML: https://mlsanity.com/paper/1510.05576/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2015.

## Built on by (most cited first, 2 of 2)

- [Posterior Sampling Reinforcement Learning with Gaussian Processes for Continuous Control: Sublinear Regret Bounds for Unbounded State Spaces](https://mlsanity.com/paper/2603.08287/) (2026)
- [Optimistic Optimization of Gaussian Process Samples](https://mlsanity.com/paper/2209.00895/) (2022)

## Abstract (arXiv)

In this paper, we consider the problem of stochastic optimization under a bandit feedback model. We generalize the GP-UCB algorithm [Srinivas and al., 2012] to arbitrary kernels and search spaces. To do so, we use a notion of localized chaining to control the supremum of a Gaussian process, and provide a novel optimization scheme based on the computation of covering numbers. The theoretical bounds we obtain on the cumulative regret are more generic and present the same convergence rates as the GP-UCB algorithm. Finally, the algorithm is shown to be empirically more efficient than its natural competitors on simple and complex input spaces.