@article{12662,
  abstract     = {Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their combinations. Multi-objective learning offers a natural framework for handling such problems without having to commit to early trade-offs. Surprisingly, statistical learning theory so far offers almost no insight into the generalization properties of multi-objective learning. In this work, we make first steps to fill this gap: We establish foundational generalization bounds for the multi-objective setting as well as generalization and excess bounds for learning with scalarizations. We also provide the first theoretical analysis of the relation between the Pareto-optimal sets of the true objectives and the Pareto-optimal sets of their empirical approximations from training data. In particular, we show a surprising asymmetry: All Pareto-optimal solutions can be approximated by empirically Pareto-optimal ones, but not vice versa.},
  author       = {Súkeník, Peter and Lampert, Christoph},
  issn         = {1433-3058},
  journal      = {Neural Computing and Applications},
  pages        = {24669–24683},
  publisher    = {Springer Nature},
  title        = {{Generalization in multi-objective machine learning}},
  doi          = {10.1007/s00521-024-10616-1},
  volume       = {37},
  year         = {2025},
}

@article{14451,
  abstract     = {We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format.},
  author       = {Cornalba, Federico and Disselkamp, Constantin and Scassola, Davide and Helf, Christopher},
  issn         = {1433-3058},
  journal      = {Neural Computing and Applications},
  number       = {2},
  pages        = {617--637},
  publisher    = {Springer Nature},
  title        = {{Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading}},
  doi          = {10.1007/s00521-023-09033-7},
  volume       = {36},
  year         = {2024},
}