# Amortized Multi-Objective Optimization Across Tasks with Generative Solution Modeling

arXiv: https://arxiv.org/abs/2511.09598 · HTML: https://mlsanity.com/paper/2511.09598/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 59 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [Few-Shot Bayesian Optimization with Deep Kernel Surrogates](https://mlsanity.com/paper/2101.07667/) (2021)
- [Pre-trained Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2109.08215/) (2021)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Sample-efficient Multi-objective Molecular Optimization with GFlowNets](https://mlsanity.com/paper/2302.04040/) (2023)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Reinforced Few-Shot Acquisition Function Learning for Bayesian Optimization](https://mlsanity.com/paper/2106.04335/) (2021)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Multi-Objective Quality Diversity Optimization](https://mlsanity.com/paper/2202.03057/) (2022)
- [Robust Model-free Reinforcement Learning with Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1910.13399/) (2019)
- [Expensive Multi-Objective Bayesian Optimization Based on Diffusion Models](https://mlsanity.com/paper/2405.08674/) (2024)
- [Transfer Learning for Bayesian Optimization on Heterogeneous Search Spaces](https://mlsanity.com/paper/2309.16597/) (2023)
- [Computational Discovery of Microstructured Composites with Optimal Stiffness-Toughness Trade-Offs](https://mlsanity.com/paper/2302.01078/) (2023)
- [(θl, θu)-Parametric Multi-Task Optimization: Joint Search in Solution and Infinite Task Spaces](https://mlsanity.com/paper/2503.08394/) (2025)
- [Parametric Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2511.05815/) (2025)

## Built on by (most cited first, 1 of 1)

- [In-Context Guidance: Learning Inter-Task Synergies via Numerical Foundational Models for Few-Shot Multitask Optimization](https://mlsanity.com/paper/2609.25836/) (2026)

## Abstract (arXiv)

Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This can be formulated as parametric expensive multi-objective optimization problems (P-EMOPs) where each task parameter defines a distinct optimization instance. Current multi-objective Bayesian optimization methods have been widely used for finding finite sets of Pareto optimal solutions for each task. However, P-EMOPs present a fundamental challenge: the continuous task parameter space can contain infinite distinct problems, each requiring separate expensive evaluations. To address this, we propose learning an inverse model to amortize the multi-objective optimization cost across the continuous task-preference space, enabling direct solution prediction for any query without the need for expensive re-evaluation. This paper introduces a novel parametric multi-objective Bayesian optimizer that learns this inverse model by alternating between (1) generative solution sampling via conditional generative models and (2) acquisition-driven search leveraging inter-task synergies. This approach enables effective optimization across multiple tasks and finally achieves direct solution prediction for unseen parameterized EMOPs without re-evaluations. We theoretically justify the faster convergence by leveraging inter-task synergies through task-aware Gaussian processes. Based on that, empirical studies in synthetic and real-world benchmarks further verify the effectiveness of the proposed parametric optimizer.