Opposition-based Multi-Objective ADAM Optimizer (OMAdam) for Training ANNs

Multi-loss functions are present in various aspects of deep learning. In multi-modal, cross-modal, and multi-task learning contexts, multi-loss functions are essential elements for handling complex data with diverse information sources. Different tasks or modalities may have conflicting objectives. By combining them into a single loss function, the model might struggle to strike the right balance between these objectives, leading to suboptimal performance. The Multi-objective Adam optimizer, also referred to as MAdam, is an extension of Adam optimizer that is applied for optimizing several competing loss functions in deep learning. The MAdam algorithm exhibits sensitivity to its initialization, necessitating the injection of ex-treme points into the initial population. Additionally, this scheme encounters difficulties in effectively capturing the disconnected and non-convex Pareto fronts. In this paper, an opposition-based scheme was introduced into MAdam framework as global search is necessary for escaping local optima in gradient-based multi-objective optimization approaches. The Opposition-based MAdam, explores multiple directions over the landscape, that leads to independence from specific initialization. In a series of experiments, we demonstrate the scalability of our method by capturing the entire Pareto front using the MNIST dataset for binary classification of digit images 2 and 3. This was achieved with a fully connected network, employing multi-objective mean absolute error and binary cross-entropy as losses. OMAdam matches Adam's Fl-score in the early generations, a result to its high exploratory capacity which enhances its performance in initial stages of classification tasks. This results in a reduction of computational costs compared to both Adam and MAdam. The variation in Fl-score values along the Pareto front trajectory enables practitioners to select a post hoc solution based on the trade-offs achieved among conflicting loss functions as multiple objectives. This contrasts with Adam, which offers limited options due to its single-solution approach.

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