Privileged Guidance for Learning Fitness Landscape Representations from Limited Observations

Learning informative fitness landscape representations from limited observations is challenging because sparse function evaluations provide only partial and sampling-sensitive views of the underlying landscape. Although richer observations, function structures, and optimizer behaviors can provide complementary landscape information, they are costly or unavailable when representing a new problem. To address this issue, we propose Privileged Guidance for Fitness Landscape Learning (PGFL), which improves low-budget representation learning by combining consistency across different limited observations with richer information available only during pretraining. Specifically, PGFL employs a landscape encoder that combines pointwise relational encoding with dimension-aware latent aggregation to obtain fixed-length representations applicable across dimensions. Multi-view alignment promotes representation consistency across different sampling designs and transformed function instances. PGFL further exploits higher-budget observations through cross-budget distillation, while function structures and optimizer behaviors provide complementary structural and behavioral supervision for the learned representations. After pretraining, all privileged information and training-only components are removed, and the frozen encoder requires only limited observations of a new function for downstream use. Experiments on the 24 noiseless BBOB functions evaluate PGFL on high-level landscape-property prediction and automated algorithm selection, together with cross-dimensional generalization, component ablations, and representation analyses. The **source code** is provided in the **supplementary material**.