#### Incentivizing Exploration with Selective Data Disclosure

##### Nicole Immorlica, Jieming Mao, Aleksandrs Slivkins, Zhiwei Steven Wu

We study the design of rating systems that incentivize (more) efficient social learning among self-interested agents. Agents arrive sequentially and are presented with a set of possible actions, each of which yields a positive reward with an unknown probability. A disclosure policy sends messages about the rewards of previously-chosen actions to arriving agents. These messages can alter agents' incentives towards exploration, taking potentially sub-optimal actions for the sake of learning more about their rewards. Prior work achieves much progress with disclosure policies that merely recommend an action to each user, but relies heavily on standard, yet very strong rationality assumptions. We study a particular class of disclosure policies that use messages, called unbiased subhistories, consisting of the actions and rewards from a subsequence of past agents. Each subsequence is chosen ahead of time, according to a predetermined partial order on the rounds. We posit a flexible model of frequentist agent response, which we argue is plausible for this class of "order-based" disclosure policies. We measure the success of a policy by its regret, i.e., the difference, over all rounds, between the expected reward of the best action and the reward induced by the policy. A disclosure policy that reveals full history in each round risks inducing herding behavior among the agents, and typically has regret linear in the time horizon $T$. Our main result is an order-based disclosure policy that obtains regret $\tilde{O}(\sqrt{T})$. This regret is known to be optimal in the worst case over reward distributions, even absent incentives. We also exhibit simpler order-based policies with higher, but still sublinear, regret. These policies can be interpreted as dividing a sublinear number of agents into constant-sized focus groups, whose histories are then revealed to future agents.

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