# Stress-Aware Learning under KL Drift via Trust-Decayed Mirror Descent

arXiv: https://arxiv.org/abs/2510.15222 · HTML: https://mlsanity.com/paper/2510.15222/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Tilted Empirical Risk Minimization](https://mlsanity.com/paper/2007.01162/) (2020)
- [Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method](https://mlsanity.com/paper/1907.02707/) (2019)
- [Online Learning with Continuous Variations: Dynamic Regret and Reductions](https://mlsanity.com/paper/1902.07286/) (2019)
- [State Entropy Regularization for Robust Reinforcement Learning](https://mlsanity.com/paper/2506.07085/) (2025)
- [ORVIT: Near-Optimal Online Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/2508.03768/) (2025)
- [Optimality of Robust Online Learning](https://mlsanity.com/paper/2304.10060/) (2023)
- [Unconstrained Robust Online Convex Optimization](https://mlsanity.com/paper/2506.12781/) (2025)
- [On the KL-Divergence-based Robust Satisficing Model](https://mlsanity.com/paper/2408.09157/) (2024)
- [Beyond KL-divergence: Risk Aware Control Through Cross Entropy and Adversarial Entropy Regularization](https://mlsanity.com/paper/2505.11068/) (2025)

## Abstract (arXiv)

We study sequential decision-making under distribution drift. We propose entropy-regularized trust-decay, which injects stress-aware exponential tilting into both belief updates and mirror-descent decisions. On the simplex, a Fenchel-dual equivalence shows that belief tilt and decision tilt coincide. We formalize robustness via fragility (worst-case excess risk in a KL ball), belief bandwidth (radius sustaining a target excess), and a decision-space Fragility Index (drift tolerated at O(√T) regret). We prove high-probability sensitivity bounds and establish dynamic-regret guarantees of tildeO(√T) under KL-drift path length ST = sumt≥2√rm KL(Dt|Dt-1)/2. In particular, trust-decay achieves O(1) per-switch regret, while stress-free updates incur Omega(1) tails. A parameter-free hedge adapts the tilt to unknown drift, whereas persistent over-tilting yields an Omega(λ2 T) stationary penalty. We further obtain calibrated-stress bounds and extensions to second-order updates, bandit feedback, outliers, stress variation, distributed optimization, and plug-in KL-drift estimation. The framework unifies dynamic-regret analysis, distributionally robust objectives, and KL-regularized control within a single stress-adaptive update.