NeurIPS 2025

ROOT: Rethinking Offline Optimization as
Distributional Translation via Probabilistic Bridge
Manh Cuong Dao∗
National University of Singapore
cuongdao@nus.edu.sg
The Hung Tran∗
Washington State University
hung.t.tran@wsu.edu
Phi Le Nguyen
Hanoi University of Science and Technology
lenp@soict.hust.edu.vn
Thao Nguyen Truong
National Institute of Advanced Industrial Science and Technology
nguyen.truong@aist.go.jp
Trong Nghia Hoang†
Washington State University
trongnghia.hoang@wsu.edu
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 distribu-
tion 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 evalu-
ated on an extensive benchmark comprising most recent methods, demonstrating
significant improvement and establishing a new state-of-the-art performance. Our
code is publicly available at https://github.com/cuong-dm/ROOT.
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Introduction
Black-box optimization arises in scientific and engineering domains where evaluating each can...