Uncertainty-Aware Offline Data-Driven Multi-Objective Optimization

Daniel Herring; Fabian Spill; Huanbo Lyu; James Andrews; Jelena Ninic; Lingfeng Wang; Miqing Li; Shiqiao Zhou; Shuo Wang; Zheming Zuo

arxiv: 2511.06459 · v2 · submitted 2025-11-09 · 💻 cs.NE

Uncertainty-Aware Offline Data-Driven Multi-Objective Optimization

Huanbo Lyu , Miqing Li , Shiqiao Zhou , Daniel Herring , Jelena Ninic , Zheming Zuo , Lingfeng Wang , James Andrews

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Fabian Spill Shuo Wang

This is my paper

Pith reviewed 2026-05-18 00:18 UTC · model grok-4.3

classification 💻 cs.NE

keywords offline data-driven optimizationmulti-objective optimizationsurrogate modelsuncertainty quantificationnon-dominated sortingevolutionary algorithmsrobust optimization

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The pith

Dual-ranking strategy prioritizes high-quality and reliable solutions by sorting on both predicted fitness and uncertainty estimates in offline multi-objective optimization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a dual-ranking strategy for offline data-driven multi-objective optimization to handle epistemic uncertainty in surrogate models. It performs non-dominated sorting using both standard surrogate fitness values and uncertainty-aware fitness values so that selected solutions score well on both quality and reliability. This addresses how uncertainty can produce incorrect dominance judgments that mislead the search. The approach is designed to work flexibly with different surrogate models rather than being restricted to Gaussian process regression. Experiments including ablations and comparisons demonstrate improved robustness in data-limited settings.

Core claim

By performing non-dominated sorting on candidate solutions using both surrogate-based fitness values and uncertainty-aware fitness values, the proposed method prioritizes candidate solutions that are simultaneously high-quality and reliable.

What carries the argument

Dual-ranking strategy that conducts separate non-dominated sortings on predictive fitness and uncertainty-adjusted fitness to combine quality and reliability in selection.

Load-bearing premise

Uncertainty estimates from the surrogate models are sufficiently accurate and well-calibrated to correct dominance judgments without introducing new biases.

What would settle it

Test the method on benchmark problems using deliberately miscalibrated surrogate uncertainty estimates and check whether performance gains over baselines disappear.

Figures

Figures reproduced from arXiv: 2511.06459 by Daniel Herring, Fabian Spill, Huanbo Lyu, James Andrews, Jelena Ninic, Lingfeng Wang, Miqing Li, Shiqiao Zhou, Shuo Wang, Zheming Zuo.

**Figure 2.** Figure 2: Workflow of the enhanced non-dominated-sorting-based MOEA, in which the improvement is contributed by our [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Pareto front obtained on DTLZ1 using surrogate-based (sur) and real (real) evaluations for all compared methods. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

read the original abstract

In offline data-driven multi-objective optimization (MOO), optimization is performed using surrogate models trained only on an offline dataset. These surrogate models contain inherent errors and uncertainty. This epistemic uncertainty can lead to incorrect dominance judgments, thereby misleading the search process. Existing methods mitigate this issue by incorporating uncertainty estimates from Gaussian Process Regression (GPR) to correct dominance judgments; however, they are restricted to GPR, and their optimization strategies cannot be scaled to other uncertainty quantification methods. In addition, GPR-based surrogates suffer from high computational cost. We propose a simple yet effective dual-ranking strategy that flexibly leverages both predictive results and uncertainty estimates from different surrogate models. By performing non-dominated sorting on candidate solutions using both surrogate-based fitness values and uncertainty-aware fitness values, the proposed method prioritizes candidate solutions that are simultaneously high-quality and reliable. Through extensive experimental evaluations, including ablation, sensitivity, and comparative experiments, we demonstrate the effectiveness and robustness of the proposed dual-ranking strategy working with different surrogates. Our dual-ranking framework offers more robust solutions for data-limited, real-world applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The dual-ranking approach extends uncertainty handling in offline MOO beyond GPR to other surrogates with decent experiments, but the exact mapping to uncertainty-aware fitness values remains underspecified and unproven for preserving dominance.

read the letter

The main takeaway is a dual-ranking method that runs non-dominated sorting twice—once on standard surrogate predictions and once on uncertainty-adjusted versions—to favor both good and reliable points in offline multi-objective optimization. It aims to work with any surrogate instead of being locked to Gaussian processes. That flexibility is the clearest step forward from the GPR-only corrections mentioned in the abstract. The experiments cover ablations, sensitivity checks, and comparisons across surrogates, which gives some practical evidence that the idea holds up in tested cases. Credit to the authors for including those runs rather than just claiming robustness. The soft spot sits in the construction of the uncertainty-aware fitness values. The abstract says they perform sorting on both sets, but it does not spell out the transformation—whether uncertainty is subtracted per objective, turned into a penalty, or handled another way. Without that detail or a check that the combined ranking still aligns with the true front when uncertainty is large, the central claim rests mostly on the empirical results. The stress-test concern lands here: if the mapping distorts trade-offs or introduces new biases, the prioritization of reliable solutions could be weaker than presented. The weakest assumption in the work is that the surrogate uncertainty estimates are well-calibrated enough to correct dominance without side effects, and the paper treats this as given rather than testing it directly. This paper is for people in evolutionary computation and surrogate-assisted optimization who face offline, data-limited problems. A reader already working on uncertainty-aware selection would pick up usable ideas from the experiments and the surrogate-agnostic framing. It deserves peer review because the core strategy is simple, the experiments are present, and referees can push on the missing mapping details and any formal consistency arguments.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a dual-ranking strategy for offline data-driven multi-objective optimization. Surrogate models are trained on a fixed offline dataset; candidate solutions are then ranked via non-dominated sorting applied simultaneously to the surrogate predictions (fitness values) and to derived uncertainty-aware fitness values. The goal is to favor solutions that are both high-quality and reliable under epistemic uncertainty. The method is presented as flexible across surrogate types (unlike prior GPR-only approaches) and is evaluated via ablation, sensitivity, and comparative experiments.

Significance. If the uncertainty-aware ranking can be shown to preserve dominance semantics with respect to the unknown true Pareto front, the approach would supply a lightweight, surrogate-agnostic mechanism for uncertainty handling in data-limited MOO. The reported flexibility with multiple surrogate families and the inclusion of ablation/sensitivity studies are positive indicators of practical utility in evolutionary computation and surrogate-assisted optimization.

major comments (2)

[§3] §3 (Method): The central claim rests on performing non-dominated sorting over both surrogate-based fitness and 'uncertainty-aware fitness values,' yet no explicit transformation is supplied that maps raw uncertainty estimates (from any surrogate) into these uncertainty-aware values. It is therefore impossible to verify whether the combined dominance relation penalizes unreliable points without distorting the original objective trade-offs or introducing new selection biases. This mapping is load-bearing for the stated advantage over existing GPR-restricted methods.
[§4] §4 (Experiments): The comparative and ablation results are described as demonstrating robustness, but without an explicit definition of the uncertainty-aware fitness construction it is unclear whether the reported gains arise from the dual-ranking mechanism itself or from incidental properties of the chosen surrogates and uncertainty estimators. A controlled check (e.g., synthetic fronts with known epistemic uncertainty) would be required to substantiate the claim that the ranking remains consistent with the true Pareto front when uncertainty is high.

minor comments (2)

[§3] Notation for the uncertainty-aware fitness vector should be introduced with a compact equation (e.g., Eq. (X)) rather than prose only; this would improve reproducibility across surrogate implementations.
[§4] Figure captions and axis labels in the experimental plots would benefit from explicit mention of which surrogate and uncertainty estimator are used in each panel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments on our manuscript. We address each of the major comments in detail below and indicate the revisions we plan to make.

read point-by-point responses

Referee: §3 (Method): The central claim rests on performing non-dominated sorting over both surrogate-based fitness and 'uncertainty-aware fitness values,' yet no explicit transformation is supplied that maps raw uncertainty estimates (from any surrogate) into these uncertainty-aware values. It is therefore impossible to verify whether the combined dominance relation penalizes unreliable points without distorting the original objective trade-offs or introducing new selection biases. This mapping is load-bearing for the stated advantage over existing GPR-restricted methods.

Authors: We appreciate the referee's emphasis on the need for an explicit mapping. In the original manuscript, the uncertainty-aware fitness is constructed by adjusting the surrogate predictions with the uncertainty estimates to favor reliable solutions, but we acknowledge that the description could be more precise. To address this, we will revise Section 3 to include a formal definition of the uncertainty-aware fitness values. For a general surrogate providing prediction ŷ_i and uncertainty σ_i for objective i, the uncertainty-aware value is defined as ŷ_i + β · σ_i (for minimization problems), where β is a hyperparameter that controls the penalty for uncertainty. This transformation is applied uniformly across surrogate types, ensuring the dual-ranking prioritizes both performance and reliability. We will also add a brief analysis showing that this does not introduce biases beyond the intended uncertainty penalization. revision: yes
Referee: §4 (Experiments): The comparative and ablation results are described as demonstrating robustness, but without an explicit definition of the uncertainty-aware fitness construction it is unclear whether the reported gains arise from the dual-ranking mechanism itself or from incidental properties of the chosen surrogates and uncertainty estimators. A controlled check (e.g., synthetic fronts with known epistemic uncertainty) would be required to substantiate the claim that the ranking remains consistent with the true Pareto front when uncertainty is high.

Authors: We agree that a more controlled validation would be beneficial to isolate the contribution of the dual-ranking strategy. Our current experimental setup uses real-world and benchmark problems with various surrogates to show robustness, but we recognize the value of synthetic tests. In the revised manuscript, we will add a new subsection in the experiments with synthetic multi-objective problems where we can control the level of epistemic uncertainty (e.g., by varying noise in the offline data). This will allow us to verify that the proposed ranking maintains alignment with the known true Pareto front under high uncertainty conditions. We believe this addition will directly address the concern and strengthen the empirical support for our claims. revision: yes

Circularity Check

0 steps flagged

No circularity detected in algorithmic proposal

full rationale

The paper presents a practical algorithmic strategy (dual-ranking via non-dominated sorting on surrogate fitness plus uncertainty-aware fitness) for offline MOO rather than any first-principles derivation or prediction that reduces to fitted inputs. No equations equate outputs to inputs by construction, no self-citation chains bear the central claim, and no ansatz or renaming is smuggled in. The method is evaluated empirically against external benchmarks, making the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard assumption that surrogate models produce usable uncertainty estimates and that non-dominated sorting on combined fitness values yields improved search behavior; no new free parameters, axioms, or invented entities are explicitly introduced in the abstract.

axioms (1)

domain assumption Surrogate models trained on offline data can produce both point predictions and meaningful uncertainty estimates that can be used to adjust dominance relations.
Invoked when the method creates uncertainty-aware fitness values for the second ranking step.

pith-pipeline@v0.9.0 · 5509 in / 1264 out tokens · 38954 ms · 2026-05-18T00:18:41.655349+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

By performing non-dominated sorting on candidate solutions using both surrogate-based fitness values and uncertainty-aware fitness values, the proposed method prioritizes candidate solutions that are simultaneously high-quality and reliable.

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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · 2 internal anchors

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Paszke, A.; Gross, S.; Massa, F.; Lerer, A.; Bradbury, J.; Chanan, G.; Killeen, T.; Lin, Z.; Gimelshein, N.; Antiga, L.; et al

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