In multi-objective learning (MOL), several possibly competing prediction tasks must be solved jointly by a single model. Achieving good trade-offs may require a model class G with larger capacity than what is necessary for solving the individual tasks. This, in turn, increases the statistical cost, as reflected in known MOL bounds that depend on the complexity of G. We show that this cost is unavoidable for some losses, even in an idealized semi-supervised setting, where the learner has access to the Bayes-optimal solutions for the individual tasks as well as the marginal distributions over the covariates. On the other hand, for objectives defined with Bregman losses, we prove that the complexity of G may come into play only in terms of unlabeled data. Concretely, we establish sample complexity upper bounds, showing precisely when and how unlabeled data can significantly alleviate the need for labeled data. This is achieved by a simple pseudo-labeling algorithm.

Multi-objective reinforcement learning (MORL) aims to optimize policies in the presence of conflicting objectives, where linear scalarization is commonly used to reduce vector-valued returns into scalar signals. While effective for certain preferences, this approach cannot capture fairness-oriented goals such as Nash social welfare or max-min fairness, which require nonlinear and non-additive trade-offs. Although several online algorithms have been proposed for specific fairness objectives, a unified approach for optimizing nonlinear welfare criteria in the offline setting--where learning must proceed from a fixed dataset--remains unexplored.

Preference-based many-objective optimization faces two obstacles: an expanding space of trade-offs and heterogeneous, context-dependent human value structures. Towards this, we propose a Bayesian framework that learns a small set of latent preference archetypes rather than assuming a single fixed utility function, modelling them as components of a Dirichlet-process mixture with uncertainty over both archetypes and their weights. To query efficiently, we designing hybrid queries that target information about (i) mode identity and (ii) within-mode trade-offs. Under mild assumptions, we provide a simple regret guarantee for the resulting mixture-aware Bayesian optimization procedure. Empirically, our method outperforms standard baselines on synthetic and real-world many-objective benchmarks, and mixture-aware diagnostics reveal structure that regret alone fails to capture.

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects.

Theproposed algorithm first formulates a multi-task learning problem as a multiobjective optimization problem, and then decomposes the multiobjective optimization problem into a set of constrained subproblems with different trade-off preferences.

To address this, some works have proposed piecewise linear scalar-izations inspired by economics [Busa-Fekete et al., 2017], while for multi-armed bandits, scalarized