arXiv:2601.23164v2 Announce Type: replace Abstract: We study the stochastic linear bandits with parameter noise model, in which the reward of action $a$ is $a^\top \theta$ where $\theta$ is sampled i.i.d. We show a regret upper bound of $\widetilde{O} (\sqrt{d T \log (K/\delta) \sigma^2_{\max})}$ for a horizon $T$, general action set of size $K$ of dimension $d$, and where $\sigma^2_{\max}$ is the maximal variance of the reward for any action. We further provide a lower bound of $\widetilde{\Omega} (d \sqrt{T \sigma^2_{\max}})$ which is tight (up to logarithmic factors) whenever $\log (K) \app
This academic paper, published on arXiv, represents routine progress in the theoretical understanding of machine learning algorithms, specifically within the field of stochastic linear bandits.
While contributing to the theoretical foundation of AI, this specific research does not present immediate practical breakthroughs or shifts relevant to strategic readers.
This paper refines theoretical bounds for a specific type of machine learning problem, incrementally improving understanding rather than changing current applications or market dynamics.
Further academic research in bandit algorithms benefits from these refined theoretical bounds.
Improved algorithmic efficiency in certain online learning scenarios could eventually result from such theoretical advancements.
Long-term, more robust and efficient AI systems, particularly in reinforcement learning, could indirectly stem from foundational work like this.
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Read at arXiv cs.LG