Optimizing Black-Box Functions via Ranking Oracles: A Provable Zeroth-Order Optimization Approach

Core Concepts

This study introduces ZO-RankSGD, a novel zeroth-order optimization algorithm that can efficiently optimize black-box functions using only ranking feedback, with theoretical guarantees on convergence.

Abstract

This paper addresses the problem of optimizing a black-box objective function when the only available feedback is a ranking oracle, which can sort a set of inputs based on the function values. This setting is particularly relevant in real-world scenarios where the objective function is evaluated by human judges.
The key contributions are:

Proposed ZO-RankSGD, a zeroth-order optimization algorithm that utilizes a novel rank-based random estimator to determine the descent direction. ZO-RankSGD is proven to converge to a stationary point.

Provided a theoretical analysis on how the characteristics of the ranking oracle, such as the number of inputs (m) and the number of ranked outputs (k), impact the variance of the gradient estimator and the overall convergence rate.

Demonstrated the effectiveness of ZO-RankSGD on various synthetic functions, as well as in the context of reinforcement learning with ranking feedback and improving the quality of images generated by a diffusion model using human ranking.

The key insights are:

Ranking oracles can provide substantial optimization-relevant information, often performing on par with value oracles.
The choice of m and k in the ranking oracle can significantly impact the optimization performance.
ZO-RankSGD offers a principled and effective approach for aligning AI systems with human preferences through ranking feedback.

Stats

The objective function f(x) is L-smooth and lower bounded by f*.
The number of inputs queried to the ranking oracle at each iteration is m.
The number of ranked outputs returned by the ranking oracle at each iteration is k.

Quotes

"Ranking data is an omnipresent feature of the internet, appearing on a variety of platforms and applications, such as search engines, social media feeds, online marketplaces, and review sites. It plays a crucial role in how we navigate and make sense of the vast amount of information available online."
"The significance of ranking data becomes even more apparent when some objective functions are evaluated through human beings, which is becoming increasingly common in various applications."

Key Insights Distilled From

Zeroth-Order Optimization Meets Human Feedback: Provable Learning via Ranking Oracles

by Zhiwei Tang,... at arxiv.org 04-16-2024

https://arxiv.org/pdf/2303.03751.pdf

Deeper Inquiries

How can the proposed ZO-RankSGD algorithm be extended to handle noisy or uncertain ranking feedback from human evaluators

To handle noisy or uncertain ranking feedback from human evaluators, the ZO-RankSGD algorithm can be extended in several ways:

Robust Estimators: Introduce robust estimators for the descent direction that are less sensitive to outliers in the ranking feedback. Techniques like robust regression or robust optimization can be employed to mitigate the impact of noisy rankings on the optimization process.

Uncertainty Modeling: Incorporate uncertainty modeling into the algorithm to account for the variability in the ranking feedback. Bayesian optimization techniques can be utilized to model the uncertainty in the rankings and adapt the optimization process accordingly.

Adaptive Sampling: Implement adaptive sampling strategies that dynamically adjust the query points based on the reliability of the ranking feedback. This can involve strategies like active learning, where the algorithm actively selects the most informative queries to reduce the impact of noisy feedback.

Ensemble Methods: Employ ensemble methods to aggregate multiple rankings and reduce the influence of individual noisy rankings. By combining multiple noisy rankings, the algorithm can obtain a more robust estimate of the true ranking order.

By incorporating these strategies, ZO-RankSGD can be enhanced to effectively handle noisy or uncertain ranking feedback, improving its robustness and performance in real-world applications.

How can the techniques from active learning be combined with ZO-RankSGD to further improve the query efficiency when optimizing with human feedback

Combining techniques from active learning with ZO-RankSGD can significantly improve query efficiency when optimizing with human feedback. Here are some ways to integrate active learning techniques:

Query Selection: Use active learning strategies to intelligently select the most informative queries for human feedback. Techniques like uncertainty sampling, query-by-committee, or expected model change can help identify the most valuable queries to optimize the objective function efficiently.

Adaptive Sampling: Dynamically adjust the sampling strategy based on the optimization progress and the quality of feedback received. Active learning algorithms can adaptively sample points in the input space to focus on regions that are most uncertain or have the potential for significant improvement.

Human-in-the-Loop Optimization: Implement a human-in-the-loop optimization framework where the algorithm iteratively refines the model based on human feedback. Active learning can guide the selection of queries to minimize the number of human evaluations required while maximizing the optimization performance.

By integrating active learning techniques, ZO-RankSGD can optimize the use of human feedback, leading to more efficient and effective optimization processes.

What are the potential applications of ZO-RankSGD beyond the ones explored in this paper, and how can it be adapted to those domains

The potential applications of ZO-RankSGD extend beyond the ones explored in the paper to various domains, including:

Marketing and Advertising: ZO-RankSGD can be applied to optimize marketing campaigns by leveraging human feedback to rank different ad creatives, messaging, or targeting strategies. This can help businesses tailor their marketing efforts to better resonate with their target audience.

Product Design: In product design, ZO-RankSGD can optimize the features of a product based on human preferences and feedback. By ranking different design options, the algorithm can iteratively improve the product to align with user preferences.

Healthcare: ZO-RankSGD can be used in healthcare settings to optimize treatment plans or interventions based on patient feedback and outcomes. By ranking different treatment options, the algorithm can personalize healthcare strategies for better patient outcomes.

Adapting ZO-RankSGD to these domains involves customizing the optimization process to suit the specific objectives and constraints of each application, while leveraging human feedback to drive iterative improvements.