# Invariance-Based Dynamic Regret Minimization

arXiv: https://arxiv.org/abs/2603.03843 · HTML: https://mlsanity.com/paper/2603.03843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 9 of 9)

- [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019)
- [Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1810.03024/) (2018)
- [A Simple Approach for Non-stationary Linear Bandits](https://mlsanity.com/paper/2103.05324/) (2021)
- [Leveraging Good Representations in Linear Contextual Bandits](https://mlsanity.com/paper/2104.03781/) (2021)
- [Invariant Policy Learning: A Causal Perspective](https://mlsanity.com/paper/2106.00808/) (2021)
- [Non-Stationary Representation Learning in Sequential Linear Bandits](https://mlsanity.com/paper/2201.04805/) (2022)
- [Meta Learning in Bandits within Shared Affine Subspaces](https://mlsanity.com/paper/2404.00688/) (2024)
- [Non-Stationary Latent Auto-Regressive Bandits](https://mlsanity.com/paper/2402.03110/) (2024)
- [Invariant Subspace Decomposition](https://mlsanity.com/paper/2404.09962/) (2024)

## Abstract (arXiv)

We consider stochastic non-stationary linear bandits where the linear parameter connecting contexts to the reward changes over time. Existing algorithms in this setting localize the policy by gradually discarding or down-weighting past data, effectively shrinking the time horizon over which learning can occur. However, in many settings historical data may still carry partial information about the reward model. We propose to leverage such data while adapting to changes, by assuming the reward model decomposes into stationary and non-stationary components. Based on this assumption, we introduce ISD-linUCB, an algorithm that uses past data to learn invariances in the reward model and subsequently exploits them to improve online performance. We show both theoretically and empirically that leveraging invariance reduces the problem dimensionality, yielding significant regret improvements in fast-changing environments when sufficient historical data is available.