# Ensemble Distributionally Robust Bayesian Optimisation with Continuous Context

arXiv: https://arxiv.org/abs/2605.07565 · HTML: https://mlsanity.com/paper/2605.07565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 14 of 14)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [Distributionally Robust Optimization and Generalization in Kernel Methods](https://mlsanity.com/paper/1905.10943/) (2019)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Multi-Period Trading via Convex Optimization](https://mlsanity.com/paper/1705.00109/) (2017)
- [First-order Conditions for Optimization in the Wasserstein Space](https://mlsanity.com/paper/2209.12197/) (2022)
- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Distributionally Robust Bayesian Quadrature Optimization](https://mlsanity.com/paper/2001.06814/) (2020)
- [Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation](https://mlsanity.com/paper/2312.10423/) (2023)
- [Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context](https://mlsanity.com/paper/2503.20341/) (2025)

## Abstract (arXiv)

We study Bayesian Optimisation (BO) in settings where the objective function is influenced by uncontrollable environmental contexts governed by an unknown probability distribution. In practice, the contextual distribution must be estimated from empirical data, a process that inherently introduces distributional mismatch, producing sub-optimal results. While Distributionally Robust Optimisation (DRO) provides a framework to mitigate these risks, existing robust BO methods frequently suffer from high computational complexity, rely on discretisation of continuous context spaces, or impose restrictive assumptions on the structure of the ambiguity set. To overcome these limitations, we propose Ensemble Distributionally Robust Bayesian Optimisation (EDRBO). Our framework leverages the expressive power of ensemble surrogate models to approximate the black-box function while simultaneously accounting for contextual uncertainty. By utilising Wasserstein ball as ambiguity sets, EDRBO provides a robustified acquisition function that remains computationally tractable and natively handles continuous context spaces. We establish a rigorous theoretical foundation for our approach by proving sublinear cumulative regret guarantees of order O(γT √T), where γT represents the maximum information gain within the ensemble. Finally, we provide extensive empirical evaluations that corroborate our theory and demonstrate the state-of-the-art performance of EDRBO.