Learning to optimize by multi-gradient for multi-objective optimization

The development of artificial intelligence for science has led to the emergence of learning-based research paradigms, necessitating a compelling reevaluation of the design of multi-objective optimization (MOO) methods. The new generation MOO methods should be rooted in automated learning rather than manual design.In this paper, we introduce a new automatic learning paradigm for optimizing MOO problems, and propose a multi-gradient learning to optimize (ML2O) method, which automatically learns a generator (or mappings) from multiple gradients to update directions.As a learning-based method, ML2O acquires knowledge of local landscapes by leveraging information from the current step and incorporates global experience extracted from historical iteration trajectory data.By introducing a new guarding mechanism, we propose a guarded multi-gradient learning to optimize (GML2O) method, and prove that the iterative sequence generated by GML2O converges to a Pareto stationary point.The experimental results demonstrate that our learned optimizer outperforms hand-designed competitors on training the multi-task learning neural network.