Stochastic and Noisy Oracles in Smooth Continuous Optimization
Read the original on arXiv Machine Learning →The article reviews models of inexact computational oracles in smooth continuous optimization, focusing on zeroth-, first-, and second-order oracles characterized by quantitative error bounds and controllable parameters. It introduces deterministic and stochastic oracle models, illustrating them with examples such as finite-difference approximations, stochastic gradients, and randomized derivative estimators, and discusses distinctions between absolute/relative errors, bias/variance, and independent/coupled randomness. The review emphasizes analytical tools that recover and compare convergence and complexity guarantees across different oracle models, providing bounds on expected stopping times and computational complexity for both deterministic and stochastic first-order methods, and briefly covering inexact second-order information.
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