Tingyang Wei

Tingyang Wei, Jiao Liu, Abhishek Gupta et al.

Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This gives rise to 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 individual tasks. However, P-EMOPs present a fundamental challenge: the continuous task parameter space can contain infinite distinct problems, each requiring separate expensive evaluations. This demands learning an inverse model that can directly predict optimized solutions for any task-preference query without expensive re-evaluation. This paper introduces the first parametric multi-objective Bayesian optimizer that learns this inverse model by alternating between (1) acquisition-driven search leveraging inter-task synergies and (2) generative solution sampling via conditional generative models. This approach enables efficient optimization across related tasks and finally achieves direct solution prediction for unseen parameterized EMOPs without additional expensive evaluations. We theoretically justify the faster convergence by leveraging inter-task synergies through task-aware Gaussian processes. Meanwhile, empirical studies in synthetic and real-world benchmarks further verify the effectiveness of our alternating framework.

Tingyang Wei, Jiao Liu, Abhishek Gupta et al.

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 ($\boldsymbolθ_l$, $\boldsymbolθ_u$), a novel ($\boldsymbolθ_l$, $\boldsymbolθ_u$)-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.