Bellman-Centric Learning: Near-Optimal Regret for Linear Bandits with Memory
We study linear bandits with memory, where past actions induce endogenous nonstationarity through an arbitrary known, bounded matrix-valued memory map. To trade off exploration and exploitation while accounting for the memory dynamics, we develop RSM-LinUCB, a Bellman-centric algorithm that learns as in linear bandits and plans as in reinforcement learning. This design admits a novel regret decomposition which separates the memory-induced error from the cumulative reward estimation error along the learner's trajectory. We prove a high-probability regret bound of $\widetilde O\big(dRS(M+1)+σd\sqrt T\big)$, where $T$ is the learning horizon, $d$ is the parameter dimension, $M$ is the memory...
| Authors | Jingyuan Liu, Huiwen Jia |
|---|---|
| Primary category | cs.LG |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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