ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge

2025-09-19

AI Summary

This work addresses offline black-box optimization—maximizing an unknown function using only a limited, static set of input-output pairs. To overcome the critical limitation of existing methods, which heavily rely on large-scale offline datasets, we reformulate the task as *directed distributional transfer* over the input space. Specifically, we construct multiple synthetic function posterior means via Gaussian processes to serve as value-guiding signals; then, we design a probabilistic bridging model that learns an invertible mapping from low-value to high-value input distributions. Optimization proceeds via inverse modeling, iteratively evolving the input distribution toward higher function values. Crucially, our framework eliminates dependence on massive offline data. Empirical evaluation on standard benchmarks demonstrates substantial improvements over state-of-the-art methods, establishing a new performance frontier in offline black-box optimization.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task. This is formulated as learning a probabilistic bridge transforming an implicit distribution of low-value inputs (i.e., offline data) into another distribution of high-value inputs (i.e., solution candidates). Such probabilistic bridge can be learned using low- and high-value inputs sampled from synthetic functions that resemble the target function. These synthetic functions are constructed as the mean posterior of multiple Gaussian processes fitted with different parameterizations on the offline data, alleviating the data bottleneck. The proposed approach is evaluated on an extensive benchmark comprising most recent methods, demonstrating significant improvement and establishing a new state-of-the-art performance.

Problem

• Optimizing black-box functions using limited offline input-output data
• Framing optimization as probabilistic distribution translation between inputs
• Overcoming data constraints via synthetic functions from Gaussian processes

Innovation

• Probabilistic bridge transforms low-value to high-value inputs
• Synthetic functions created from Gaussian processes posterior
• Alleviates data bottleneck via distributional translation approach