Sharp bounds for stochastic proximal and projection estimators via radial dominance
Proving how accurately random methods can solve convex optimization problems
Mathematicians have proven sharp bounds on how well stochastic methods can approximate solutions to convex optimization problems—the kind used constantly in machine learning and engineering. The work uses a technique called radial dominance to show exactly how the error shrinks as you add more random samples, and proves these rates are the best possible.
Optimization algorithms power everything from training neural networks to portfolio design, but engineers have long worked without knowing if their chosen method is efficient or wasteful. These bounds tell practitioners when stochastic approximation methods will work well and when the error rates are guaranteed tight—eliminating guesswork about algorithm quality.