  We study a variant of online convex optimization where the player is
permitted to switch decisions at most $S$ times in expectation throughout $T$
rounds. Similar problems have been addressed in prior work for the discrete
decision set setting, and more recently in the continuous setting but only with
an adaptive adversary. In this work, we aim to fill the gap and present
computationally efficient algorithms in the more prevalent oblivious setting,
establishing a regret bound of $O(T/S)$ for general convex losses and
$\widetilde O(T/S^2)$ for strongly convex losses. In addition, for stochastic
i.i.d.~losses, we present a simple algorithm that performs $\log T$ switches
with only a multiplicative $\log T$ factor overhead in its regret in both the
general and strongly convex settings. Finally, we complement our algorithms
with lower bounds that match our upper bounds in some of the cases we consider.
