  We present a polynomial-time algorithm for online differentially private
synthetic data generation. For a data stream within the hypercube $[0,1]^d$ and
an infinite time horizon, we develop an online algorithm that generates a
differentially private synthetic dataset at each time $t$. This algorithm
achieves a near-optimal accuracy bound of $O(\log(t)t^{-1/d})$ for $d\geq 2$
and $O(\log^{4.5}(t)t^{-1})$ for $d=1$ in the 1-Wasserstein distance. This
result extends the previous work on the continual release model for counting
queries to Lipschitz queries. Compared to the offline case, where the entire
dataset is available at once, our approach requires only an extra polylog
factor in the accuracy bound.
