Proves it is impossible to achieve optimal last-iterate rates for GD and SGD without knowing the horizon T in advance, incurring an unavoidable poly-log factor penalty even in the deterministic case.
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Stochastic Krasnoselskii-Mann iterations converge almost surely and with rates under finite variance at a single fixed point rather than uniform variance bounds, recovering optimal complexity and providing first such results for some splitting methods.
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Gradient Descent's Last Iterate is Often (slightly) Suboptimal
Proves it is impossible to achieve optimal last-iterate rates for GD and SGD without knowing the horizon T in advance, incurring an unavoidable poly-log factor penalty even in the deterministic case.
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Stochastic Krasnoselskii-Mann Iterations: Convergence without Uniformly Bounded Variance
Stochastic Krasnoselskii-Mann iterations converge almost surely and with rates under finite variance at a single fixed point rather than uniform variance bounds, recovering optimal complexity and providing first such results for some splitting methods.