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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper investigates the problem of online learning for minimizing a generalized version of swap regret. More precisely, the authors consider the notion of conditional swap regret, where the swap regret is defined for a stronger adversary than usual in the sense that the adversary's action depends on the past sequence of the player. In particular, when the memory size of the adversary is restricted to k, the regret is called the k-gram conditional regret. The authors propose prediction strategies with a k-gram conditional regret of O(\sqrt{N^k T log N}) and state-dependent regret bound, respectively. Moreover, using the conditional swap regret, the authors defines the conditional correlated equilibrium and shows a convergence result.