Learning to Defer in Non-Stationary Time Series via Switching State-Space Models

TL;DR

This paper introduces L2D-SLDS, an online learning-to-defer framework for non-stationary time series that adaptively balances expert input and learner updates, outperforming existing methods on multiple benchmarks.

Contribution

The paper proposes a novel switching state-space model for online learning-to-defer in non-stationary settings, with theoretical regret guarantees and practical improvements.

Findings

L2D-SLDS defers on less than 2% of rounds in real datasets.

It outperforms or matches non-stationary bandit baselines.

The model effectively updates beliefs about experts in non-stationary environments.

Abstract

Learning-to-defer (L2D) routes each decision to a system's own predictor or to an external expert. Streaming time-series settings break the offline-L2D assumptions: the data are non-stationary, expert availability shifts over time, and the internal predictor is trained online. We propose L2D-SLDS, a one-stage online L2D framework based on a factorized switching linear-Gaussian state-space model over all potential residuals: a discrete regime, a shared global factor, and per-expert idiosyncratic states. The always-observed internal residual continuously updates beliefs about every unqueried expert through the shared factor, and a learner-aware query score balances immediate cost against latent-state information gain and one-step learner improvement. We prove an oracle inequality against a time-varying learn-and-defer comparator, decomposing regret into a query-bonus budget, an SLDS predictive-cost-error term~$\mathcal{E}_{\mathrm{SLDS}}$, and the internal learner's interval dynamic regret. On synthetic, Melbourne, Jena, and 24-expert Delhi benchmarks, L2D-SLDS is competitive with or improves on contextual- and non-stationary-bandit baselines while deferring on ${<}2\%$ of real-data rounds.