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Incrementality, which is used to measure the causal effect of showing an adto a potential customer (e.g. a user in an internet platform) versus not, is acentral object for advertisers in online advertising platforms. This paperinvestigates the problem of how an advertiser can learn to optimize the biddingsequence in an online manner \emph{without} knowing the incrementalityparameters in advance. We formulate the offline version of this problem as aspecially structured episodic Markov Decision Process (MDP) and then, for itsonline learning counterpart, propose a novel reinforcement learning (RL)algorithm with regret at most $\widetilde{O}(H^2\sqrt{T})$, which depends onthe number of rounds $H$ and number of episodes $T$, but does not depend on thenumber of actions (i.e., possible bids). A fundamental difference between ourlearning problem from standard RL problems is that the realized reward feedbackfrom conversion incrementality is \emph{mixed} and \emph{delayed}. To handlethis difficulty we propose and analyze a novel pairwise moment-matchingalgorithm to learn the conversion incrementality, which we believe is ofindependent of interest.

Incrementality Bidding via Reinforcement Learning under Mixed and Delayed Rewards