I am reading the proof of Theorem 1.1. of Elad Hazan, Introduction to Online Convex Optimization. It is not making sense to me. Given any deterministic algorithm the adversary can always choose the opposite action at each step. Thus no deterministic algorithm can guarantee even one single correct action. There must be some condition that is not explicitly spelled out in the setting, or I have missed something obvious. Can someone elucidate?
2026-05-16 14:31:23.1778941883
Best deterministic algorithm makes twice the mistakes the best expert makes
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