algorithms-optimization / Convex optimization
Carefully designed stepsize schedules alone accelerate plain gradient descent beyond its textbook O(1/T) rate, without momentum. Whether they can reach the optimal O(T^-2) was open. A lower bound of Omega(T^-1.9319) for last-iterate convergence under predetermined nonnegative stepsize schedules says they cannot.
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Recorded as partial: the bound is Omega(T^-1.9319) against an achievable O(T^-1.2716), so it rules out reaching the optimal rate without pinning down the true one.
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Carefully designed stepsize schedules alone accelerate plain gradient descent beyond its textbook O(1/T) rate, without momentum. Whether they can reach the optimal O(T^-2) was open. A lower bound of Omega(T^-1.9319) for last-iterate convergence under predetermined nonnegative stepsize schedules says they cannot.
Recorded as partial: the bound is Omega(T^-1.9319) against an achievable O(T^-1.2716), so it rules out reaching the optimal rate without pinning down the true one.
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