arXiv:2602.06902v2 Announce Type: replace Abstract: In this paper, we study dynamic regret in unconstrained online convex optimization (OCO) with movement costs. Specifically, we generalize the standard setting by allowing the movement cost coefficients $\lambda_t$ to vary arbitrarily over time. Our main contribution is a novel algorithm that establishes the first comparator-adaptive dynamic regret bound for this setting, guaranteeing $\widetilde{\mathcal{O}}(\sqrt{(M^2+MP_T)(T+\sum_t \lambda_t)})$ regret, where $P_T$ is the path length of the comparator sequence over $T$ rounds and $M$ is the
This research addresses a fundamental challenge in online convex optimization, a field seeing rapid advances as AI systems become more autonomous and need to adapt to dynamic environments.
Improved parameter-free algorithms for online learning with varying costs and delayed feedback are crucial for developing more robust and efficient AI agents operating in complex, real-world conditions.
The development of a novel algorithm for unconstrained online convex optimization with time-varying movement costs and delayed feedback promises more adaptable and performant AI systems.
- · AI developers
- · Robotics companies
- · Autonomous systems
- · Logistics and supply chain optimization
- · Traditional static optimization approaches
- · Systems unprepared for dynamic environments
More efficient and adaptable AI agents capable of operating with less human intervention will be developed.
This improved algorithmic capability could accelerate the deployment of AI in critical infrastructure and complex operational environments.
Reduced operational overhead and increased performance of AI in dynamic settings might lead to new levels of automation across various industries.
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