Abstract
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 O(√T) under KL-drift path length S_T = Σ_t≥2√ KL(D_t|D_t-1)/2. In particular, trust-decay achieves O(1) per-switch regret, while stress-free updates incur Ω(1) tails. A parameter-free hedge adapts the tilt to unknown drift, whereas persistent over-tilting yields an Ω(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.