Global Convergence Rate Analysis of a Generic Line Search Algorithm with Noise

In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and gradient estimates are inexact possibly random. The assumed to be bounded in absolute without any additional assumptions. We extend the framework based on stochastic methods from [C. Cartis K. Scheinberg, Math. Program., 169 (2018), pp. 337--375] which was developed provide standard exact function values random gradients case noisy functions. introduce two alternative conditions which, when satisfied some sufficiently large probability at each iteration, guarantees properties method. derive expected complexity bounds reach near optimal neighborhood convex, strongly convex nonconvex dependence specified.