Online Learning and Unlearning: Efficient Algorithms with Near-Optimal Regret Guarantees

Abstract: We formalize online learning-unlearning (OLU) in the Online Convex Optimization (OCO) setting, where a learner updates a model sequentially on a stream of convex losses while accommodating occasional unlearning requests between updates. We require that after a deletion, the distribution of all future outputs is statistically indistinguishable from that of a learner trained on the same stream with the deleted data removed. We propose two OLU algorithms based on Online Gradient Descent (OGD). Passive OLU leverages the contractive dynamics of OGD and injects calibrated noise, incurring no additional computation beyond standard OGD; however, its regret depends on the deletion schedule. We then introduce a schedule-robust variant that mitigates this dependence. Active OLU employs an offline unlearning algorithm to actively steer the online iterate toward the corresponding retrained trajectory. Under standard convexity and smoothness assumptions, our methods achieve regret comparable to standard OGD, demonstrating that strong online unlearning guarantees can be achieved with minimal loss in learning performance.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Chicheng_Zhang1

Submission Number: 8383