[Paper] QUIVER: Cost-Aware Adaptive Preference Querying in Surrogate-Assisted Evolutionary Multi-Objective Optimization

Source: arXiv - 2605.04267v1

Overview

The paper introduces QUIVER, a new algorithm that blends cheap objective evaluations with smart, cost‑aware preference queries to steer evolutionary multi‑objective optimization (EMO). By treating both evaluation and preference‑elicitation as budget items, QUIVER learns how and when to ask a decision‑maker for input, dramatically reducing the regret (i.e., the gap between the solution presented and the true optimal trade‑off) on challenging benchmark problems.

Key Contributions

• Cost‑aware decision‑making loop – Formulates the selection of the next action (evaluate a solution or ask a preference query) as a utility‑per‑cost maximization problem.
• Heterogeneous query handling – Supports multiple query modalities: cheap, noisy pairwise preference statements (PS) and richer, more expensive indifference adjustments (IA).
• Adaptive query mix – QUIVER automatically shifts the balance between PS and IA depending on problem difficulty, achieving up to a 25 % reduction in final utility regret versus single‑modality baselines.
• Surrogate‑assisted EMO integration – Couples the query policy with a surrogate model that predicts objective values, keeping the expensive true evaluations to a minimum.
• Extensive empirical validation – Benchmarked on DTLZ and WFG suites with synthetic decision‑maker models, showing consistent superiority on the harder WFG problems.

Methodology

1. Problem Setting – The optimizer must find a solution that maximizes an unknown scalarized utility function defined by a decision‑maker (DM). The DM can be queried in two ways:

   • Pairwise Preference (PS): “Do you prefer solution A over B?” – cheap but noisy.
   • Indifference Adjustment (IA): “Adjust the trade‑off so that these two solutions become equally attractive.” – more informative but costlier.

2. Surrogate Model – A Gaussian‑process‑style surrogate predicts the multi‑objective outcomes of candidate solutions, providing both mean estimates and uncertainty.

3. Query‑Informed Value Estimation for Regret (QUIVER) Loop

   • Action candidates: (i) evaluate a candidate solution on the true expensive objectives, (ii) ask a PS query, (iii) ask an IA query.
   • Expected improvement per cost: For each candidate action, QUIVER estimates the expected reduction in decision‑quality regret (how much closer the DM’s true optimum will be identified) and divides it by the known cost of that action.
   • Selection: The action with the highest ratio is executed.

4. Budget Management – The total budget is a fixed sum of evaluation‑cost units and query‑cost units. QUIVER stops when the budget is exhausted, returning the solution with the highest estimated utility.

Results & Findings

• Query mix adapts to difficulty: On the easy DTLZ2 problem, QUIVER spends ~80 % of its query budget on PS (cheap, noisy) and only 20 % on IA. On the hard WFG9 problem, the split flips to ~35 % PS and 65 % IA, showing that richer queries become worthwhile when the search space is more complex.
• Surrogate efficiency: By relying on the surrogate for most evaluations, QUIVER reduces the number of true expensive objective calls by up to 60 % compared with a vanilla EMO baseline.
• Robustness to noise: Even when PS responses are deliberately noisy, QUIVER’s cost‑aware policy still outperforms static‑policy baselines.

Practical Implications

• Interactive design tools – Engineers using multi‑objective CAD or hyper‑parameter tuning interfaces can let QUIVER decide whether to ask quick “which design looks better?” questions or more involved “adjust the trade‑off” dialogs, keeping user fatigue low while converging faster to a satisfactory design.
• Resource‑constrained optimization – In domains where objective evaluations are expensive (e.g., CFD simulations, hardware prototyping), QUIVER’s surrogate‑driven budget allocation can cut down on costly runs by up to half, delivering comparable or better solutions.
• Automated ML pipelines – When tuning models across accuracy, latency, and memory, QUIVER can query a data‑science stakeholder for preferences only when the extra information justifies the time cost, leading to faster deployment cycles.
• Customizable cost models – The framework lets teams plug in their own cost estimates (e.g., monetary cost of a cloud simulation, human time for a UI survey), making QUIVER adaptable to many industrial settings.

Limitations & Future Work

• Synthetic DM models – Experiments rely on simulated decision‑makers; real‑world user studies are needed to confirm that the adaptive query mix behaves similarly with actual humans.
• Scalability of surrogate – The current Gaussian‑process surrogate may struggle with very high‑dimensional objective spaces (>50 dimensions); exploring scalable surrogates (e.g., deep ensembles) is a natural next step.
• Fixed query cost assumption – QUIVER treats PS and IA costs as static values; in practice, user fatigue or computational overhead can vary dynamically, suggesting a richer cost‑model extension.
• Extension to more query types – Incorporating other preference elicitation modalities (e.g., ranking, trade‑off sliders) could further improve efficiency on complex problems.

Overall, QUIVER demonstrates that a cost‑aware, adaptive approach to preference querying can make interactive multi‑objective optimization both cheaper and more user‑friendly, opening the door to smarter decision‑support tools across engineering and AI.

Authors

• Florian A. D. Burnat

Paper Information

• arXiv ID: 2605.04267v1
• Categories: cs.LG, cs.NE, math.OC
• Published: May 5, 2026
• PDF: Download PDF