Offline Stochastic Optimization of Black-Box Objective Functions

TL;DR

This work introduces Stochastic Offline BBO (SOBBO), which optimizes a black-box objective under uncontrollable stochasticity using only offline data. It presents two regime-specific solutions: Estimate-Then-Differentiate (ETD) for large-data settings, which learns a differentiable surrogate and uses its gradient to perform standard gradient-based optimization with a consistency guarantee; and Deep Gradient Interpolation (DGI) for scarce-data settings, which directly learns a conservative gradient field enforcing balance, reconstruction, and path-independence to yield robust gradient estimates. Theoretical results establish the consistency of ETD's gradient estimates, and extensive experiments on synthetic benchmarks and real-world tasks show that both ETD and DGI outperform baselines, with DGI delivering particularly strong gradient accuracy under data scarcity. Overall, the approach bridges offline data-driven learning with stochastic optimization, enabling efficient, reliable design optimization when function evaluations are expensive and randomness is pervasive.

Abstract

Many challenges in science and engineering, such as drug discovery and communication network design, involve optimizing complex and expensive black-box functions across vast search spaces. Thus, it is essential to leverage existing data to avoid costly active queries of these black-box functions. To this end, while Offline Black-Box Optimization (BBO) is effective for deterministic problems, it may fall short in capturing the stochasticity of real-world scenarios. To address this, we introduce Stochastic Offline BBO (SOBBO), which tackles both black-box objectives and uncontrolled uncertainties. We propose two solutions: for large-data regimes, a differentiable surrogate allows for gradient-based optimization, while for scarce-data regimes, we directly estimate gradients under conservative field constraints, improving robustness, convergence, and data efficiency. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world tasks.

Figures (11)

• Figure 1: This work considers stochastic optimization of a black-box objective function from only historical data.
• Figure 2: Our proposed methods learn to interpolate the true (unobserved) gradient with an offline dataset, and subsequently generate gradient estimates to be employed by various gradient-based techniques to find the optimal design.
• Figure 3: Gradient Estimation for Scarce-Data Regime. Top figures show cosine similarity (higher is better); gradient norm distance (lower is better) in bottom figures.
• Figure 4: Gradient Estimation for Large-Data Regime. Cosine similarity and norm distance on Quadratic (top), and Griewank (bottom) objective functions.
• Figure 5: Ablation studies on the effects of the balance weight (left), number of sampled paths (middle), and integration accuracymeasured by the integration steps (right) on the performance of gradient estimation.

Theorems & Definitions (6)

• Theorem 3.1
• proof : Proof of Theorem \ref{['thm:consistency-of-gradient']}
• Lemma 4.1
• proof : Proof of Lemma \ref{['lemma:validity-of-recon-loss']}
• proof : Proof of Theorem \ref{['thm:consistency-of-gradient']}
• proof : Proof of Lemma \ref{['lemma:validity-of-recon-loss']}