A new paper explores the impact of approximation errors in Online Mirror Descent (OMD), a core algorithm for optimization and machine learning. The research reveals a complex relationship between the smoothness of the regularizer used and the algorithm's robustness to these errors. Specifically, while uniformly smooth regularizers have a tight bound on excess regret, barrier regularizers like negative entropy on the simplex are sensitive to approximation errors, requiring exponentially small errors to avoid linear regret. However, negative entropy regains robustness with stochastic losses on the simplex, though this benefit does not extend to all subsets. AI
IMPACT This research provides theoretical insights into the practical limitations of optimization algorithms used in machine learning.
RANK_REASON The cluster contains a peer-reviewed academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
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