WebDec 7, 2024 · In this paper, we conduct a systematic study of quantum query lower bounds on finding ϵ-approximate stationary points of nonconvex functions, and we consider the following two important settings: 1) having access to p-th order derivatives; or 2) having access to stochastic gradients. WebAug 12, 2024 · As a general approach you could try to find a minimum point. y = ln ( 1 − 0.5 u). Differentiating, y ′ = log ( 2) 0.5 u 1 − u 0.5. To find stationary points, set equal to zero …
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Webdeterministic pth-order methods achieve the upper bounds, and the lower bounds apply to all randomized … WebLower Bounds for Finding Stationary Points II: First-Order Methods. Yair Carmon, John Duchi, Oliver Hinder and Aaron Sidford. Mathematical programming, 2024. See a summary of both lower bounds in our Neurips workshop paper. Interior point methods for problems with nonconvex constraints the guns of navarone 1961 film
Lower Bounds for Finding Stationary Points II: First-Order …
WebFeb 10, 2024 · Surprisingly, even for this seemingly restricted class, finding an ϵ-stationary point, i.e., a point ¯ x for which d (0, ∂ f (¯ x)) ≤ ϵ, is intractable. In other words, no algorithm can guarantee to find an ϵ-stationary point within a finite number of iterations. This intractability suggests that, to obtain meaningful non-asymptotic ... WebHowever, the low-dimensional complexity of computing stationary points remains open. Indeed, the main limitation ofCarmon et al.(2024) is that their lower bound constructions require the ambient dimension to be large: more precisely, they require d (1="2) for deterministic algorithms, and d (1e ="4) for randomized algorithms. The large ... WebDec 5, 2024 · We lower bound the complexity of finding ϵ-stationary points (with gradient norm at most ϵ) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased stochastic gradient oracle with bounded variance, we prove that (in the worst case) any … the barn antiques balsall common