# (θl, θu)-Parametric Multi-Task Optimization: Joint Search in Solution and Infinite Task Spaces

arXiv: https://arxiv.org/abs/2503.08394 · HTML: https://mlsanity.com/paper/2503.08394/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 82 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Effective Diversity in Population Based Reinforcement Learning](https://mlsanity.com/paper/2002.00632/) (2020)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Quality Diversity for Multi-task Optimization](https://mlsanity.com/paper/2003.04407/) (2020)
- [Half a Dozen Real-World Applications of Evolutionary Multitasking, and More](https://mlsanity.com/paper/2109.13101/) (2021)
- [A Scalable Test Problem Generator for Sequential Transfer Optimization](https://mlsanity.com/paper/2304.08503/) (2023)
- [Towards Safe Multi-Task Bayesian Optimization](https://mlsanity.com/paper/2312.07281/) (2023)
- [Evolutionary Multitasking for Multiobjective Continuous Optimization: Benchmark Problems, Performance Metrics and Baseline Results](https://mlsanity.com/paper/1706.02766/) (2017)
- [Multitask Learning with No Regret: from Improved Confidence Bounds to Active Learning](https://mlsanity.com/paper/2308.01744/) (2023)
- [Parametric-Task MAP-Elites](https://mlsanity.com/paper/2402.01275/) (2024)
- [Controller Adaptation via Learning Solutions of Contextual Bayesian Optimization](https://mlsanity.com/paper/2403.04881/) (2024)
- [A Two stage Adaptive Knowledge Transfer Evolutionary Multi-tasking Based on Population Distribution for Multi/Many-Objective Optimization](https://mlsanity.com/paper/2001.00810/) (2020)

## Built on by (most cited first, 4 of 4)

- [Amortized Multi-Objective Optimization Across Tasks with Generative Solution Modeling](https://mlsanity.com/paper/2511.09598/) (2025)
- [Towards Efficient Evaluation of Evolutionary Transfer Optimization: Case Studies on Task-Parameterized Applications](https://mlsanity.com/paper/2609.05040/) (2026)
- [Solving Few-Shot Multiobjective Multitask Optimization via Iterative Sequential Transfer](https://mlsanity.com/paper/2609.11228/) (2026)
- [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)

Multi-task optimization is typically characterized by a fixed and finite set of tasks. The present paper relaxes this condition by considering a non-fixed and potentially infinite set of optimization tasks defined in a parameterized, continuous and bounded task space. We refer to this unique problem setting as parametric multi-task optimization (PMTO). Assuming the bounds of the task parameters to be (boldsymbolθl, boldsymbolθu), a novel (boldsymbolθl, boldsymbolθu)-PMTO algorithm is crafted to operate in two complementary modes. In an offline optimization mode, a joint search over solution and task spaces is carried out with the creation of two approximation models: (1) for mapping points in a unified solution space to the objective spaces of all tasks, which provably accelerates convergence by acting as a conduit for inter-task knowledge transfers, and (2) for probabilistically mapping tasks to their corresponding solutions, which facilitates evolutionary exploration of under-explored regions of the task space. In the online mode, the derived models enable direct optimization of any task within the bounds without the need to search from scratch. This outcome is validated on both synthetic test problems and practical case studies, with the significant real-world applicability of PMTO shown towards fast reconfiguration of robot controllers under changing task conditions. The potential of PMTO to vastly speedup the search for solutions to minimax optimization problems is also demonstrated through an example in robust engineering design.