  Time-series forecasting (TSF) finds broad applications in real-world
scenarios. Due to the dynamic nature of time-series data, it is crucial to
equip TSF models with out-of-distribution (OOD) generalization abilities, as
historical training data and future test data can have different distributions.
In this paper, we aim to alleviate the inherent OOD problem in TSF via
invariant learning. We identify fundamental challenges of invariant learning
for TSF. First, the target variables in TSF may not be sufficiently determined
by the input due to unobserved core variables in TSF, breaking the conventional
assumption of invariant learning. Second, time-series datasets lack adequate
environment labels, while existing environmental inference methods are not
suitable for TSF.
  To address these challenges, we propose FOIL, a model-agnostic framework that
enables timeseries Forecasting for Out-of-distribution generalization via
Invariant Learning. FOIL employs a novel surrogate loss to mitigate the impact
of unobserved variables. Further, FOIL implements a joint optimization by
alternately inferring environments effectively with a multi-head network while
preserving the temporal adjacency structure, and learning invariant
representations across inferred environments for OOD generalized TSF. We
demonstrate that the proposed FOIL significantly improves the performance of
various TSF models, achieving gains of up to 85%.
