[Paper Review] Movement Penalized Bayesian Optimization with Application to Wind Energy Systems

Shyam Sundhar Ramesh, Pier Giuseppe Sessa+2 more|arXiv (Cornell University)|Oct 14, 2022

Gaussian Processes and Bayesian Inference4 citations

TL;DR

This paper proposes Movement Penalized Bayesian Optimization (GP-MD), a novel contextual Bayesian optimization algorithm that integrates mirror descent with Gaussian Process confidence bounds to minimize both service cost and movement costs in sequential decision-making. It achieves superior performance over standard CBO methods in wind energy applications by explicitly penalizing costly altitude changes, demonstrating significant gains in energy efficiency while reducing operational movement costs.

ABSTRACT

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.

Motivation & Objective

• To address the limitation of standard contextual Bayesian optimization (CBO) in real-world applications where frequent action changes incur high operational costs.
• To formalize the episodic contextual Bayesian optimization problem with movement costs as a metrical task system (MTS) under a metric distance function.
• To develop a randomized mirror descent algorithm that balances exploration, exploitation, and movement cost minimization using Gaussian Process confidence bounds.
• To provide rigorous regret guarantees for the proposed algorithm under noisy bandit feedback and arbitrary context sequences.
• To evaluate the method on real-world airborne wind energy (AWE) systems, demonstrating improved energy generation and reduced movement costs.

Proposed method

• Proposes a novel randomized mirror descent algorithm that combines online learning strategies from Coester and Lee (2019a) with Gaussian Process (GP) confidence bounds for uncertainty quantification.
• Uses a metric-based movement cost function to penalize large or frequent changes in actions, modeling the physical cost of reconfiguring systems like AWE turbines.
• Employs a dual-optimization strategy: minimizing service cost (e.g., energy generation) while constraining action changes via a movement penalty parameter ρ.
• Derives regret bounds that scale with the square root of the maximum information gain (γ) and logarithmic terms in δ and H, ensuring theoretical performance guarantees.
• Applies the algorithm to real-world AWE data across multiple geographic locations and time periods, using a discrete-time energy generation model with movement energy loss.
• Uses a union bound over multiple probabilistic events (Lemmas 1, 65, 46) to ensure high-probability regret bounds with confidence 1−δ.

Experimental results

Research questions

• RQ1 Can a contextual Bayesian optimization framework be extended to explicitly penalize movement costs in sequential decision-making?
• RQ2 How can online learning techniques for metrical task systems be integrated with Gaussian Process models to balance exploration, exploitation, and action stability?
• RQ3 What is the theoretical regret performance of a movement-penalized CBO algorithm under noisy bandit feedback and arbitrary context sequences?
• RQ4 How does the proposed algorithm compare to standard CBO and movement-conservative baselines in real-world wind energy applications?
• RQ5 To what extent does movement penalization improve energy efficiency in airborne wind energy systems with costly altitude adjustments?

Key findings

• GP-MD outperforms standard CBO (CGP-LCB) in total energy generation across all tested locations, particularly when movement costs are non-negligible.
• At Loc. 1 (Lat. 53, Long. -10), GP-MD achieved higher energy output than CGP-LCB for low ρ values (favoring service cost), with a 12% improvement in energy generation at ρ=4.
• At Loc. 2 (Lat. 53, Long. -4), GP-MD consistently outperformed CGP-LCB across a range of ρ values, showing robustness to varying wind conditions and cost trade-offs.
• At Loc. 3 (Lat. 47, Long. 6), GP-MD achieved a 15% increase in total energy generation compared to CGP-LCB at ρ=4, demonstrating strong performance under different atmospheric conditions.
• The algorithm achieved a regret bound of O(β_{Nep}(H²Nepγ_{HNep} + H log(H/δ))^{1/2} + H(B+ψ)log(Nep log(Nep)/δ)), proving theoretical convergence under uncertainty.
• The method reduced movement costs by up to 40% compared to CGP-LCB while maintaining or improving service cost performance, validating the effectiveness of movement penalization.