# Movement Penalized Bayesian Optimization with Application to Wind Energy Systems

arXiv: https://arxiv.org/abs/2210.08087 · HTML: https://mlsanity.com/paper/2210.08087/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 14 Oct 2022.

## Builds on (most cited first, 26 of 26)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [On Online Learning in Kernelized Markov Decision Processes](https://mlsanity.com/paper/1911.01871/) (2019)
- [Batched Gaussian Process Bandit Optimization via Determinantal Point Processes](https://mlsanity.com/paper/1611.04088/) (2016)
- [Beyond Online Balanced Descent: An Optimal Algorithm for Smoothed Online Optimization](https://mlsanity.com/paper/1905.12776/) (2019)
- [Smoothed Online Optimization for Regression and Control](https://mlsanity.com/paper/1810.10132/) (2018)
- [Chasing Nested Convex Bodies Nearly Optimally](https://mlsanity.com/paper/1811.00999/) (2018)
- [Chasing Convex Bodies Optimally](https://mlsanity.com/paper/1905.11968/) (2019)
- [No-Regret Learning in Unknown Games with Correlated Payoffs](https://mlsanity.com/paper/1909.08540/) (2019)
- [Learning to Play Sequential Games versus Unknown Opponents](https://mlsanity.com/paper/2007.05271/) (2020)
- [Chasing Convex Bodies with Linear Competitive Ratio](https://mlsanity.com/paper/1905.11877/) (2019)
- [SnAKe: Bayesian Optimization with Pathwise Exploration](https://mlsanity.com/paper/2202.00060/) (2022)
- [Scaling Gaussian Process Optimization by Evaluating a Few Unique Candidates Multiple Times](https://mlsanity.com/paper/2201.12909/) (2022)
- [Online Optimization with Predictions and Non-convex Losses](https://mlsanity.com/paper/1911.03827/) (2019)
- [Metrical task systems on trees via mirror descent and unfair gluing](https://mlsanity.com/paper/1807.04404/) (2018)
- [Contextual Games: Multi-Agent Learning with Side Information](https://mlsanity.com/paper/2107.06327/) (2021)
- [Cost-aware Multi-objective Bayesian optimisation](https://mlsanity.com/paper/1909.03600/) (2019)
- [Mixed Strategies for Robust Optimization of Unknown Objectives](https://mlsanity.com/paper/2002.12613/) (2020)
- [Competitively Chasing Convex Bodies](https://mlsanity.com/paper/1811.00887/) (2018)
- [Pure entropic regularization for metrical task systems](https://mlsanity.com/paper/1906.04270/) (2019)
- [Bayesian optimization for modular black-box systems with switching costs](https://mlsanity.com/paper/2006.02624/) (2020)

## Built on by (most cited first, 7 of 7)

- [Bayesian optimization as a flexible and efficient design framework for sustainable process systems](https://mlsanity.com/paper/2401.16373/) (2024)
- [Transition Constrained Bayesian Optimization via Markov Decision Processes](https://mlsanity.com/paper/2402.08406/) (2024)
- [MONGOOSE: Path-wise Smooth Bayesian Optimisation via Meta-learning](https://mlsanity.com/paper/2302.11533/) (2023)
- [Bayesian Optimisation Against Climate Change: Applications and Benchmarks](https://mlsanity.com/paper/2306.04343/) (2023)
- [Practical Path-based Bayesian Optimization](https://mlsanity.com/paper/2312.00622/) (2023)
- [The Traveling Bandit: A Framework for Bayesian Optimization with Movement Costs](https://mlsanity.com/paper/2410.14533/) (2024)
- [Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions](https://mlsanity.com/paper/2504.20527/) (2025)

## Abstract (arXiv)

Contextual Bayesian optimization (CBO) is a powerful framework for sequential decision-making given side information, with important applications, e.g., in wind energy systems. In this setting, the learner receives context (e.g., weather conditions) at each round, and has to choose an action (e.g., turbine parameters). Standard algorithms assume no cost for switching their decisions at every round. However, in many practical applications, there is a cost associated with such changes, which should be minimized. We introduce the episodic CBO with movement costs problem and, based on the online learning approach for metrical task systems of Coester and Lee (2019), propose a novel randomized mirror descent algorithm that makes use of Gaussian Process confidence bounds. We compare its performance with the offline optimal sequence for each episode and provide rigorous regret guarantees. We further demonstrate our approach on the important real-world application of altitude optimization for Airborne Wind Energy Systems. In the presence of substantial movement costs, our algorithm consistently outperforms standard CBO algorithms.