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Follow-the-Leader (FTL) is an intuitive sequential prediction strategy thatguarantees constant regret in the stochastic setting, but has terribleperformance for worst-case data. Other hedging strategies have betterworst-case guarantees but may perform much worse than FTL if the data are notmaximally adversarial. We introduce the FlipFlop algorithm, which is the firstmethod that provably combines the best of both worlds.  As part of our construction, we develop AdaHedge, which is a new way ofdynamically tuning the learning rate in Hedge without using the doubling trick.AdaHedge refines a method by Cesa-Bianchi, Mansour and Stoltz (2007), yieldingslightly improved worst-case guarantees. By interleaving AdaHedge and FTL, theFlipFlop algorithm achieves regret within a constant factor of the FTL regret,without sacrificing AdaHedge's worst-case guarantees.  AdaHedge and FlipFlop do not need to know the range of the losses in advance;moreover, unlike earlier methods, both have the intuitive property that theissued weights are invariant under rescaling and translation of the losses. Thelosses are also allowed to be negative, in which case they may be interpretedas gains.

Follow the Leader If You Can, Hedge If You Must