# Robust Bayesian Satisficing

arXiv: https://arxiv.org/abs/2308.08291 · HTML: https://mlsanity.com/paper/2308.08291/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 16 Aug 2023.

## Builds on (most cited first, 13 of 13)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Satisficing in Time-Sensitive Bandit Learning](https://mlsanity.com/paper/1803.02855/) (2018)
- [Bayesian optimisation under uncertain inputs](https://mlsanity.com/paper/1902.07908/) (2019)
- [Stochastic Bandits with Context Distributions](https://mlsanity.com/paper/1906.02685/) (2019)
- [Lenient Regret and Good-Action Identification in Gaussian Process Bandits](https://mlsanity.com/paper/2102.05793/) (2021)
- [Satisficing in multi-armed bandit problems](https://mlsanity.com/paper/1512.07638/) (2015)
- [Lenient Regret for Multi-Armed Bandits](https://mlsanity.com/paper/2008.03959/) (2020)
- [ESCADA: Efficient Safety and Context Aware Dose Allocation for Precision Medicine](https://mlsanity.com/paper/2111.13415/) (2021)

## Built on by (most cited first, 3 of 3)

- [Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2506.01625/) (2025)
- [Nearly-Optimal Algorithm for Adversarial Kernelized Bandits](https://mlsanity.com/paper/2605.10299/) (2026)
- [Statistical Properties of Robust Satisficing](https://mlsanity.com/paper/2405.20451/) (2024)

## Abstract (arXiv)

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning. To overcome this challenge, robust satisficing (RS) seeks a robust solution to an unspecified distributional shift while achieving a utility above a desired threshold. This paper focuses on the problem of RS in contextual Bayesian optimization when there is a discrepancy between the true and reference distributions of the context. We propose a novel robust Bayesian satisficing algorithm called RoBOS for noisy black-box optimization. Our algorithm guarantees sublinear lenient regret under certain assumptions on the amount of distribution shift. In addition, we define a weaker notion of regret called robust satisficing regret, in which our algorithm achieves a sublinear upper bound independent of the amount of distribution shift. To demonstrate the effectiveness of our method, we apply it to various learning problems and compare it to other approaches, such as distributionally robust optimization.