Search Results - "Drusvyatskiy, Dmitriy"

Stochastic Subgradient Method Converges on Tame Functions by Davis, Damek, Drusvyatskiy, Dmitriy, Kakade, Sham, Lee, Jason D.

“…This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove…”
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Stochastic algorithms with geometric step decay converge linearly on sharp functions by Davis, Damek, Drusvyatskiy, Dmitriy, Charisopoulos, Vasileios

“…Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially…”
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Proximal Methods Avoid Active Strict Saddles of Weakly Convex Functions by Davis, Damek, Drusvyatskiy, Dmitriy

“…We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly…”
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Low-Rank Matrix Recovery with Composite Optimization: Good Conditioning and Rapid Convergence by Charisopoulos, Vasileios, Chen, Yudong, Davis, Damek, Díaz, Mateo, Ding, Lijun, Drusvyatskiy, Dmitriy

“…The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem…”
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Conservative and Semismooth Derivatives are Equivalent for Semialgebraic Maps by Davis, Damek, Drusvyatskiy, Dmitriy

“…Subgradient and Newton algorithms for nonsmooth optimization require generalized derivatives to satisfy subtle approximation properties: conservativity for the…”
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The nonsmooth landscape of phase retrieval by Davis, Damek, Drusvyatskiy, Dmitriy, Paquette, Courtney

“…Abstract We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions a simple…”
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A note on alternating projections for ill-posed semidefinite feasibility problems by Drusvyatskiy, Dmitriy, Li, Guoyin, Wolkowicz, Henry

“…We observe that Sturm’s error bounds readily imply that for semidefinite feasibility problems, the method of alternating projections converges at a rate of O (…”
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Generic nondegeneracy in convex optimization by DRUSVYATSKIY, DMITRIY, LEWIS, ADRIAN S.

“…lower- \mathbf{C}^2 functions…”
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Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods by Drusvyatskiy, Dmitriy, Lewis, Adrian S.

“…The proximal gradient algorithm for minimizing the sum of a smooth and nonsmooth convex function often converges linearly even without strong convexity. One…”
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Asymptotic normality and optimality in nonsmooth stochastic approximation by Davis, Damek, Drusvyatskiy, Dmitriy, Jiang, Liwei

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Subgradient Methods for Sharp Weakly Convex Functions by Davis, Damek, Drusvyatskiy, Dmitriy, MacPhee, Kellie J., Paquette, Courtney

“…Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp…”
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Efficient Quadratic Penalization Through the Partial Minimization Technique by Aravkin, Aleksandr Y., Drusvyatskiy, Dmitriy, van Leeuwen, Tristan

“…Common computational problems, such as parameter estimation in dynamic models and partial differential equation (PDE)-constrained optimization, require data…”
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Sweeping by a tame process by Daniilidis, Aris, Drusvyatskiy, Dmitriy

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The euclidean distance degree of orthogonally invariant matrix varieties by Drusvyatskiy, Dmitriy, Lee, Hon-Leung, Ottaviani, Giorgio, Thomas, Rekha R.

“…The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Euclidean distance degree…”
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Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions by Drusvyatskiy, Dmitriy, Ioffe, Alexander D., Lewis, Adrian S.

“…Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally…”
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The slope robustly determines convex functions by Daniilidis, Aris, Drusvyatskiy, Dmitriy

“…We show that the deviation between the slopes of two convex functions controls the deviation between the functions themselves. This result reveals that the…”
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Gradient descent with adaptive stepsize converges (nearly) linearly under fourth-order growth by Davis, Damek, Drusvyatskiy, Dmitriy, Jiang, Liwei

“…A prevalent belief among optimization specialists is that linear convergence of gradient descent is contingent on the function growing quadratically away from…”
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The radius of statistical efficiency by Cutler, Joshua, Díaz, Mateo, Drusvyatskiy, Dmitriy

“…Classical results in asymptotic statistics show that the Fisher information matrix controls the difficulty of estimating a statistical model from observed…”
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Projection methods for quantum channel construction by Drusvyatskiy, Dmitriy, Li, Chi-Kwong, Pelejo, Diane Christine, Voronin, Yuen-Lam, Wolkowicz, Henry

“…We consider the problem of constructing quantum channels, if they exist, that transform a given set of quantum states { ρ 1 , … , ρ k } to another such set { ρ…”
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Conservative and semismooth derivatives are equivalent for semialgebraic maps by Davis, Damek, Drusvyatskiy, Dmitriy

“…Subgradient and Newton algorithms for nonsmooth optimization require generalized derivatives to satisfy subtle approximation properties: conservativity for the…”
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