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  1. Free, publicly-accessible full text available December 16, 2025
  2. Free, publicly-accessible full text available December 16, 2025
  3. Free, publicly-accessible full text available December 16, 2025
  4. We introduce a technique for tuning the learning rate scale factor of any base optimization algorithm and schedule automatically, which we call Mechanic. Our method provides a practical realization of recent theoretical reductions for accomplishing a similar goal in online convex optimization. We rigorously evaluate Mechanic on a range of large scale deep learning tasks with varying batch sizes, schedules, and base optimization algorithms. These experiments demonstrate that depending on the problem, Mechanic either comes very close to, matches or even improves upon manual tuning of learning rates. 
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  5. We study variants of the online linear optimization (OLO) problem with bandit feedback, where the algorithm has access to external information about the unknown cost vector. Our motivation is the recent body of work on using such “hints” towards improving regret bounds for OLO problems in the full-information setting. Unlike in the full-information OLO setting, with bandit feedback, we first show that one cannot improve the standard regret bounds of O(\sqrt{T}) by using hints, even if they are always well-correlated with the cost vector. In contrast, if the algorithm is empowered to issue queries and if all the responses are correct, then we show O(\log(T)) regret is achievable. We then show how to make this result more robust — when some of the query responses can be adversarial — by using a little feedback on the quality of the responses. 
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