Model Assessment and Selection under Temporal Distribution Shift

We investigate model assessment and selection in a changing environment, by synthesizing datasets from both the current time period and historical epochs. To tackle unknown and potentially arbitrary temporal distribution shift, we develop an adaptive rolling window approach to estimate the generalization error of a given model. This strategy also facilitates the comparison between any two candidate models by estimating the difference of their generalization errors. We further integrate pairwise comparisons into a single-elimination tournament, achieving near-optimal model selection from a collection of candidates. Theoretical analyses and numerical experiments demonstrate the adaptivity of our proposed methods to the non-stationarity in data.

A Stability Principle for Learning under Non-Stationarity

We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while keeping the cumulative bias within an acceptable range relative to the stochastic error. Our theory showcases the adaptability of this approach to unknown non-stationarity. The regret bound is minimax optimal up to logarithmic factors when the population losses are strongly convex, or Lipschitz only. At the heart of our analysis lie two novel components: a measure of similarity between functions and a segmentation technique for dividing the non-stationary data sequence into quasi-stationary pieces.