Efficient Mathematical Methods for the Optimization of Large and Complex Systems
[Technical Report, Final Report]
REGENTS OF THE UNIVERSITY OF CALIFORNIA
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This project studies complex large-scale optimization problems, numerical algorithm, and applications in machine learning, optimal control, transportation, and power systems. A summary of some of our results developed during the last performance period is provided belowProjection-free online convex optimization We considered structured online convex optimization OCO with bandit feedback, where either the loss function is smooth or the constraint set is strongly convex. Projection- free methods are among the most popular and computationally efficient algorithms for solving this problem, mainly due to their ability to handle convex constraints appearing in machine learning for which computing projections is often impractical in high-dimensional settings. Despite the improved regret bound results for the full-information setting where the gradients of the functions are readily available, it remains unclear whether simple projection-free zero-order algorithms become more efficient for structured OCO problems in the case when multiple function values can be sampled at each time instance.
- Operations Research
- Statistics and Probability