报告人：江波 教授（上海财经大学）

时间：2026年06月21日 14:00-

地点：数统学院LD718

摘要：In this talk, we revisit a classical adaptive stepsize strategy for gradient descent: the Polyak stepsize (PolyakGD), originally proposed in Polyak (1969). We study the convergence behavior of PolyakGD from two perspectives: tight worst-case analysis and universality across function classes. As our first main result, we establish the tightness of the known convergence rates of PolyakGD by explicitly constructing worst-case functions. In particular, we show that the O((1 − 1/κ1)^K) rate for smooth strongly convex functions and the O(1/K) rate for smooth convex functions are both tight. Moreover, we theoretically show that PolyakGD automatically exploits floating-point errors to escape the worst-case behavior. Our second main result provides new convergence guarantees for PolyakGD under both H¨older smoothness and H¨older growth conditions. These findings show that the Polyak stepsize is universal, automatically adapting to various function classes without requiring prior knowledge of problem parameters.

邀请人：蒋 杰

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