IOP: An Idempotent-Like Optimization Method on the Pareto Front of Hypernetwork

Pareto Front Learning (PFL) has been one of the effective means to resolve multi-objective optimization problems through exploring all optimal solutions to learn the entire Pareto front. Pareto Hypernetwork (PHN) is a new promising way to generate the sequence of Pareto-optimal solutions that can be further used as potential solutions to constitute the Pareto front. However, the existing PHN-based approaches suffer from two performance issues: They take as inputs human-crafted preference vector or chunk embedding, rather than the input data samples, and thus vulnerable to data distribution shifts. Such approaches cannot optimize all potential solutions when forming the Pareto front, as they merely optimize the loss pertaining to one single input at a time of optimization round. To improve the quality of the Pareto front, we propose IOP, a novel Idempotent-like Optimization method to learn the entire Pareto front accurately and enhance Hypernetwork's adaptability to distribution shifts. In particular, IOP performs idempotent-like optimization by exploiting manifold space mapping, so that the target networks generated by the optimized Hypernetwork can effectively handle samples with similar distributions of the input samples, without the pre-defined human-crafted inputs. IOP maximizes the Hypervolume indicator that is composed of all potential solutions at a higher level. Experimental results demonstrate that IOP outperforms the state-of-the-art methods by 4.7% on average in producing the Pareto front and has a 10.5% improvement in adaptability.