Privacy-Aware Sequential Learning
Sequential learning often relies on individuals reporting private information, with early reports shaping later beliefs and collective decisions. When such reports are sensitive, privacy protection creates a fundamental trade-off in the design of sequential feedback systems. We study this trade-off as a platform design problem: before reporting begins, the platform commits to a local privacy-preserving reporting protocol, seeking to improve final-decision accuracy while limiting the time required to accumulate sufficient evidence. Surprisingly, privacy protection can accelerate learning. With continuous Gaussian signals, smooth randomized response under metric differential privacy preserves asymptotic learning and yields a public log-likelihood ratio growing at rate $Θ_{\varepsilon}(\log n)$, faster than the nonprivate $Θ(\sqrt{\log n})$ benchmark, substantially reducing high-confidence stopping times. With heterogeneous privacy parameters, learning can be faster still; when privacy budgets are uniformly distributed on $[0,1]$, public belief grows at rate $Θ(n^{1/4})$. With binary signals, randomized response generates a nonmonotone relationship between privacy and decision accuracy because privacy affects both report informativeness and cascade thresholds. Stopping time can also be nonmonotone because stronger privacy reduces report informativeness while encouraging participation. Overall, privacy is not merely a constraint on information release, but a platform design lever shaping participation, stopping, and collective learning.