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This paper introduces the hypervolume maximization with a single solution asan alternative to the mean loss minimization. The relationship between the twoproblems is proved through bounds on the cost function when an optimal solutionto one of the problems is evaluated on the other, with a hyperparameter tocontrol the similarity between the two problems. This same hyperparameterallows higher weight to be placed on samples with higher loss when computingthe hypervolume's gradient, whose normalized version can range from the meanloss to the max loss. An experiment on MNIST with a neural network is used tovalidate the theory developed, showing that the hypervolume maximization canbehave similarly to the mean loss minimization and can also provide betterperformance, resulting on a 20% reduction of the classification error on thetest set.

Single-Solution Hypervolume Maximization and its use for Improving Generalization of Neural Networks