How effective are discrete-continuous multi-task learning compared to single-output models? Insights from travel mode and departure time analysis

In travel behaviour research, joint modelling exercises capturing the interdependencies among multiple decisions have predominantly relied on theory-driven econometric models. While data-driven techniques hold significant promise, existing studies predominantly focus on discrete-discrete output models, neglecting the complexity of mixed decision types inherent in travel behaviour. Many interdependent travel decisions involve mixed decision types; for example, travel mode choice is discrete, while departure time is continuous. Ignoring these inherent dynamics may lead to biased model estimations and flawed policy implications. This underscores the need for joint ML approaches that accommodate discrete–continuous decision scenarios. In this study, we develop artificial neural networks (ANNs) to jointly model travel mode as a discrete choice and departure time as a continuous variable. The jointness is achieved by using shared hidden layers in the neural network, allowing the model to learn common features that influence both travel mode choice and departure time. At first, we evaluate two ANN architectures: hard-parameter sharing (HP-MTL), which involves shared layers and task-specific layers within the ANN, and cross-stitch (CS-MTL), which introduces a more flexible sharing mechanism by learning weighted combinations of activations from task-specific layers. Both models are compared against single-output neural network (SO-NNx) and econometric models, with additional evaluation of prediction speed across synthetic datasets of varying sizes. The results show that the CS-MTL (i.e., more complex architecture) performed almost similarly to SO-NNx in most performance measures but did worse than the HP-MTL, likely due to negative learning , where increased complexity does not improve performance given the nature of the task interdependencies. For departure time prediction, HP-MTL improved the R 2 by 21.4 % and reduced the mean squared error (MSE) by 8.3 % compared to the SO-NNx and achieved 4.7-fold and 27 % improvements over the hazard model. In travel mode choice, HP-MTL delivered modest accuracy gains overall—with a particularly ∼10 % improvement for transit mode predictions. In contrast, more sophisticated MTL architectures adapted mainly from computer vision performed worse than the SO-NNx. In terms of speed, HP-MTL was 35–45 % faster than SO-NNx, while econometric models were about 2 times faster. The findings of this research add capacity to transportation modelling literature in exploring, using, and assessing the suitability of using ML to model joint discrete–continuous decisions.

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