Research map / Optimization / Nonconvex and smooth optimization
Local Curvature Descent: Squeezing More Curvature out of Standard and Polyak Gradient Descent
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Proposes Local Curvature Descent, a gradient method with adaptive stepsizes that use local curvature information (without Hessian computation) for convex optimization, applied to standard and Polyak gradient descent.
Problem
Convex optimization with stepsizes that are more powerful and adaptive than standard fixed or classical choices, without paying the cost of full second-order methods that need Hessians.
Approach
Observes that for some problems (e.g., minimizing sums of squares of absolutely convex functions) local curvature can be exploited cheaply to set stepsizes, giving a Hessian-free curvature-aware variant of gradient descent and of Polyak stepsize gradient descent.
Experimental setup
Baselines: standard gradient descent Polyak gradient descent
Builds on: Polyak stepsize gradient descent
Closest papers by meaning
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