Privacy-Aware Sequential Learning

TL;DR

This paper explores how privacy-preserving strategies in sequential learning can surprisingly accelerate information aggregation, balancing privacy and accuracy, especially with continuous signals and heterogeneous populations.

Contribution

It introduces an optimal randomization strategy that enhances learning speed under privacy constraints, contrasting with traditional nonprivate models.

Findings

Privacy-preserving noise accelerates learning to logarithmic time.

Under privacy, the expected time to correct actions becomes finite.

Heterogeneous populations can achieve near-optimal learning rates with some low-privacy agents.

Abstract

In settings like vaccination registries, individuals act after observing others, and the resulting public records can expose private information. We study privacy-preserving sequential learning, where agents add endogenous noise to their reported actions to conceal private signals. Efficient social learning relies on information flow, seemingly in conflict with privacy. Surprisingly, with continuous signals and a fixed privacy budget $(\epsilon)$, the optimal randomization strategy balances privacy and accuracy, accelerating learning to $\Theta_{\epsilon}(\log n)$, faster than the nonprivate $\Theta(\sqrt{\log n})$ rate. In the nonprivate baseline, the expected time to the first correct action and the number of incorrect actions diverge; under privacy with sufficiently small $\epsilon$, both are finite. Privacy helps because, under the false state, agents more often receive signals contradicting the majority; randomization then asymmetrically amplifies the log-likelihood ratio, enhancing aggregation. In heterogeneous populations, an order-optimal $\Theta(\sqrt{n})$ rate is achievable when a subset of agents have low privacy budgets. With binary signals, however, privacy reduces informativeness and impairs learning relative to the nonprivate baseline, though the dependence on $\epsilon$ is nonmonotone. Our results show how privacy reshapes information dynamics and inform the design of platforms and policies.