# Stochastic Process Bandits: Upper Confidence Bounds Algorithms via Generic Chaining

arXiv: https://arxiv.org/abs/1602.04976 · HTML: https://mlsanity.com/paper/1602.04976/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2016.

## 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)
- [Bandits on graphs and structures](https://mlsanity.com/paper/2605.03493/) (2026)

## Abstract (arXiv)

The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his operability over a continuous domain. The theoretical framework applies to functions under weak probabilistic smoothness assumptions and also extends significantly the spectrum of application of UCB strategies. Moreover generic regret bounds are derived which are then specialized to Gaussian processes indexed on infinite-dimensional spaces as well as to quadratic forms of Gaussian processes. Lower bounds are also proved in the case of Gaussian processes to assess the optimality of the proposed algorithm.