 Our bounds are optimal up to \text{poly(\log\log n+\log(1/\epsilon)) factors, and improve the 1{\epsilon^3} dependence of }  Ben-Eliezer et  al.
<meaning-changed>  Our bounds are optimal up to \text{poly(\log\log n+\log(1/\epsilon)) factors, and improve the 1{\epsilon^3} dependence of }  Ben-Eliezer et  al.
 Our bounds are optimal up to \text{poly(\log\log n+\log(1/\epsilon)) factors, and improve the 1{\epsilon^3} dependence of } In the adversarially robust streaming model, a stream of elements is presented to an algorithm and is allowed to depend on the output of the algorithm at earlier times during the stream. In the classic insertion-only model of data streams, Ben-Eliezer et al.