Constrained Preferential Bayesian Optimization and Its Application in Banner Ad Design

TL;DR

This work extends preferential Bayesian optimization (PBO) to constrained settings by introducing constrained preferential Bayesian optimization (CPBO) and a new acquisition, expected utility of the best option with constraints (EUBOC). CPBO learns a GP surrogate for the objective from pairwise human preferences while enforcing a constraint via a second GP and the joint-feasibility acquisition, effectively focusing search within feasible regions. The authors validate CPBO through synthetic benchmarks and a banner ad design task, where the constraint is a predicted click-through rate (CTR); results show accelerated convergence and higher feasibility compared to baselines, with warm-starting improving efficiency. They further demonstrate a designer-in-the-loop framework that integrates CTR considerations with designer preferences, and report positive feedback from professional ad designers, highlighting reduced workload and improved design guidance, thereby illustrating practical potential for constraint-aware human-in-the-loop design optimization.

Abstract

Preferential Bayesian optimization (PBO) is a variant of Bayesian optimization that observes relative preferences (e.g., pairwise comparisons) instead of direct objective values, making it especially suitable for human-in-the-loop scenarios. However, real-world optimization tasks often involve inequality constraints, which existing PBO methods have not yet addressed. To fill this gap, we propose constrained preferential Bayesian optimization (CPBO), an extension of PBO that incorporates inequality constraints for the first time. Specifically, we present a novel acquisition function for this purpose. Our technical evaluation shows that our CPBO method successfully identifies optimal solutions by focusing on exploring feasible regions. As a practical application, we also present a designer-in-the-loop system for banner ad design using CPBO, where the objective is the designer's subjective preference, and the constraint ensures a target predicted click-through rate. We conducted a user study with professional ad designers, demonstrating the potential benefits of our approach in guiding creative design under real-world constraints.

Figures (15)

• Figure 1: Two-dimensional test function used for evaluation. (a) Objective function. The star represents the maximum. (b) Constraint function overlaid onto the objective function. The lightly shaded white areas indicate infeasible regions, and the star represents the optimal solution that satisfies the constraint.
• Figure 2: Result of the test function setting. The Optimality gap for (a) 2D and (c) 6D test functions, where the horizontal axis represents the iteration steps and the vertical axis represents the Optimality gap (lower is better). The Feasible for (b) 2D and (d) 6D test functions, where the vertical axis represents the Feasible (higher is better), the lines denote the mean, and the lightly shaded areas denote the standard deviation.
• Figure 3: Result of the banner ad design application setting. (a) Image gap (lower is better) and (b) Feasible (higher is better).
• Figure 4: Concept of our designer-in-the-loop banner ad design framework. The designer provides feedback to the system about preferences, and the system predicts the CTRs. The system then updates the surrogate models and proposes new design candidates using our CPBO technique.
• Figure 5: User interface of our banner ad design system in color editing mode. This system provides pairs of design candidates for each iteration.