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

arXiv: https://arxiv.org/abs/2601.22538 · HTML: https://mlsanity.com/paper/2601.22538/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 112 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019)
- [Mostly Exploration-Free Algorithms for Contextual Bandits](https://mlsanity.com/paper/1704.09011/) (2017)
- [Online Learning with Feedback Graphs: Beyond Bandits](https://mlsanity.com/paper/1502.07617/) (2015)
- [Who Should Predict? Exact Algorithms For Learning to Defer to Humans](https://mlsanity.com/paper/2301.06197/) (2023)
- [Ensemble Sampling](https://mlsanity.com/paper/1705.07347/) (2017)
- [Learning to Defer to Multiple Experts: Consistent Surrogate Losses, Confidence Calibration, and Conformal Ensembles](https://mlsanity.com/paper/2210.16955/) (2022)
- [A Change-Detection based Framework for Piecewise-stationary Multi-Armed Bandit Problem](https://mlsanity.com/paper/1711.03539/) (2017)
- [Sample Efficient Learning of Predictors that Complement Humans](https://mlsanity.com/paper/2207.09584/) (2022)
- [Principled Approaches for Learning to Defer with Multiple Experts](https://mlsanity.com/paper/2310.14774/) (2023)
- [Recurrent switching linear dynamical systems](https://mlsanity.com/paper/1610.08466/) (2016)
- [Regression with Multi-Expert Deferral](https://mlsanity.com/paper/2403.19494/) (2024)
- [In Defense of Softmax Parametrization for Calibrated and Consistent Learning to Defer](https://mlsanity.com/paper/2311.01106/) (2023)
- [Realizable H-Consistent and Bayes-Consistent Loss Functions for Learning to Defer](https://mlsanity.com/paper/2407.13732/) (2024)
- [Cardinality-Aware Set Prediction and Top-k Classification](https://mlsanity.com/paper/2407.07140/) (2024)
- [Particle Gibbs with Ancestor Sampling](https://mlsanity.com/paper/1401.0604/) (2014)
- [A Two-Stage Learning-to-Defer Approach for Multi-Task Learning](https://mlsanity.com/paper/2410.15729/) (2024)
- [Adversarial Robustness in Two-Stage Learning-to-Defer: Algorithms and Guarantees](https://mlsanity.com/paper/2502.01027/) (2025)
- [Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer](https://mlsanity.com/paper/2506.20650/) (2025)
- [Optimal Query Allocation in Extractive QA with LLMs: A Learning-to-Defer Framework with Theoretical Guarantees](https://mlsanity.com/paper/2410.15761/) (2024)
- [A Causal Framework for Evaluating Deferring Systems](https://mlsanity.com/paper/2405.18902/) (2024)
- [Budgeted Multiple-Expert Deferral](https://mlsanity.com/paper/2510.26706/) (2025)
- [Learning-to-defer for sequential medical decision-making under uncertainty](https://mlsanity.com/paper/2109.06312/) (2021)
- [An Information-Theoretic Analysis of Nonstationary Bandit Learning](https://mlsanity.com/paper/2302.04452/) (2023)

## Built on by (most cited first, 6 of 6)

- [Beyond Augmented-Action Surrogates for Multi-Expert Learning-to-Defer](https://mlsanity.com/paper/2604.09414/) (2026)
- [Consistent Learning-to-Defer with Expert-Conditional Advice](https://mlsanity.com/paper/2603.14324/) (2026)
- [Optimized Deferral for Imbalanced Settings](https://mlsanity.com/paper/2604.27723/) (2026)
- [Online Learning-to-Defer with Varying Experts](https://mlsanity.com/paper/2605.12340/) (2026)
- [Mind the Gap: Structure-Aware Consistency in Preference Learning](https://mlsanity.com/paper/2604.27733/) (2026)
- [A Query Is Not a Commitment: Learning to Correct Expert Answers in Online Deferral](https://mlsanity.com/paper/2610.07084/) (2026)

## Abstract (arXiv)

Learning-to-defer (L2D) lets a predictor decide, at each round, whether to issue its own forecast or pay for an expert's. In non-stationary time series this decision must keep adapting, although deployment reveals only the consulted expert's forecast while a historical archive records every expert with the target. L2D-SLDS learns from this archive a switching state-space model of the target and all expert forecasts, whose shared and expert-specific states describe how experts move together and apart. Its predictive law supplies the internal forecast and the expected cost of every consultation, which a greedy router minimizes, and one consultation also updates the beliefs about unconsulted and unavailable experts. We prove sublinear regret against a changing conditional-risk oracle without exploration, when the candidate models are accurate and either the archive separates them or live feedback reveals cost differences. On three real datasets, L2D-SLDS has the lowest cost among eight bandit routers and adapts its consultation rate to the fee.