Gaussian process boosts budget allocation efficiency under constraints
Gaussian Process Bandits for Constraint Black Box Lever Optimization
Machine Learning
Summary
When trying to split a limited budget across different groups, it can be hard to figure out the best way to do it because feedback is often slow, noisy, and limited. The authors propose using a kind of smart guessing method called Gaussian Process Upper Confidence Bound (GP-UCB) that learns by sharing knowledge across similar options, making it faster to find good solutions. They tested this approach with simulated data and in a real-world experiment, showing it works better than simpler methods. This helps improve decision-making when adjusting budgets in challenging, noisy environments.
What this means in practice
- •For advertising campaign managers: Optimize allocation of advertising budgets across segments under noisy and delayed feedback to improve campaign efficiency.
- •For online platform operators: Improve automated resource allocation across user segments with limited intervention opportunities using smoother learning from aggregated outcomes.
Authors
Bram van den Akker, Hidde Fokkema, Anastasiia Kornilova
Abstract
Optimizing discrete allocation weights across competing segments of a shared budget is a fundamental challenge in resource-constrained, sequential decision-making environments. In practice, this optimization is often hindered by delayed, noisy, and aggregate feedback, alongside strict operational constraints on how frequently weights can be adjusted. Because of the resulting combinatorial action space and extreme data sparsity, classical multi-armed bandit algorithms that evaluate arms independently are rendered highly inefficient. To overcome these limitations, we propose a segmentation-agnostic approach utilizing Gaussian Process Upper Confidence Bound (GP-UCB) algorithms. By placing a Gaussian Process prior on the reward function, our method effectively shares information across neighboring configurations, drastically reducing the necessary exploration horizon. In this paper, we bridge the gap between theoretical bandit research and production-scale deployment. We first introduce a high-fidelity synthetic simulator to evaluate various kernel configurations under stationary, drifting, and reactive environments, identifying a composite Matérn + Linear kernel as the most robust choice for overcoming local noise and global shifts. Finally, we validate our findings through a large-scale Randomized Controlled Trial (RCT) in a live production environment. Our empirical results demonstrate that the GP-UCB approach delivers a statistically significant efficiency lift compared to a standard $\varepsilon$-greedy baseline, offering a highly practical solution for real-world black-box lever optimization.