($oldsymbol{ heta}_l, oldsymbol{ heta}_u$)-Parametric Multi-Task Optimization: Joint Search in Solution and Infinite Task Spaces

2025-03-11

AI Summary

This work addresses the limitation of conventional multi-task optimization—where the task set is fixed and finite—by introducing Parameterized Multi-Task Optimization (PMTO): jointly optimizing task selection and solution search over a continuous, bounded, and potentially infinite parameterized task space. Methodologically, we propose a dual-agent surrogate framework: (i) a cross-task objective mapping model enabling knowledge transfer, and (ii) a probabilistic task-to-solution mapping model facilitating active exploration of the task space; the framework integrates evolutionary algorithms, Gaussian process regression, and probabilistic task embedding for synergistic optimization. Experiments on synthetic benchmarks and robotic controller reconfiguration demonstrate significant improvements in generalization efficiency: the approach achieves second-level optimal responses to arbitrary new tasks within predefined bounds and shows promising acceleration for robust engineering design problems formulated as minimax optimization.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Multi-task optimization is typically characterized by a fixed and finite set of optimization 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 ($oldsymbol{ heta}_l$, $oldsymbol{ heta}_u$), a novel ($oldsymbol{ heta}_l$, $oldsymbol{ heta}_u$)-PMTO algorithm is crafted to enable joint search over tasks and their solutions. This joint search is supported by two approximation models: (1) for mapping solutions 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 the solution space, which facilitates evolutionary exploration of under-explored regions of the task space. At the end of a full ($oldsymbol{ heta}_l$, $oldsymbol{ heta}_u$)-PMTO run, the acquired models enable rapid identification of optimized solutions for any task lying within the specified bounds. 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.

Problem

• Extends multi-task optimization to infinite, parameterized task spaces.
• Develops a joint search algorithm for tasks and solutions.
• Enables rapid solution identification within specified task bounds.

Innovation

• Joint search in solution and task spaces.
• Approximation models for inter-task knowledge transfer.
• Rapid solution identification for bounded tasks.