Minimax Rate

Minimax rates represent the optimal achievable error in statistical estimation problems, providing a benchmark for algorithm performance. Current research focuses on refining these rates for various settings, including distributionally robust optimization, score-based generative models, and best-arm identification in bandit problems, often leveraging techniques like adaptive algorithms and novel notions of sparsity to improve efficiency. Determining minimax rates is crucial for understanding fundamental limits in statistical learning and for designing algorithms that approach these limits, impacting fields ranging from machine learning to causal inference. The development of tighter bounds and algorithms achieving these rates is a significant ongoing effort.