arXiv:2605.29748v1 Announce Type: cross Abstract: We study the Lipschitz bandit problem, where a learner sequentially maximizes an unknown Lipschitz function $f$ over a domain $\mathcal{X} \subset [0,1]^d$ using noisy pointwise evaluations. Existing regret bounds are either worst-case, scaling as $\tilde{\Theta} \left ( T^{d+1/d+2}\right )$, or adaptive via the zooming dimension $d_z$, yielding $\tilde{\Theta} \left ( T^{d_z+1/d_z+2}\right )$. However, such zooming-based guarantees are only partially instance-dependent, as they depend solely on the asymptotic growth of near-optimal level sets
This research addresses fundamental limitations in optimization algorithms, particularly relevant for AI and machine learning fields facing increasingly complex, high-dimensional problems.
Improved Lipschitz bandit algorithms could lead to more efficient and robust machine learning models, reducing computational cost and accelerating discovery in various applications.
The theoretical understanding and practical performance of sequential optimization algorithms for unknown functions could be enhanced, potentially leading to faster algorithmic convergence.
- · AI researchers
- · Machine learning developers
- · Optimisation software providers
- · Inefficient heuristic approaches
More efficient training and deployment of AI models requiring sequential decision-making under uncertainty.
Accelerated development cycles for new AI applications and potentially reduced compute requirements for certain tasks.
These advancements could contribute to the broader efficiency of AI systems, potentially impacting the compute and energy bottlenecks in the long run.
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Read at arXiv cs.LG