\section{Concluding Remarks}
In this work, we propose an adaptation of Hedge for the partitioning experts setting where the number of experts increases polynomially with time.
%\sout{is growing with time at an exponential rate}. 
We show that our algorithm and its adaptive rate variant have (near-)optimal expected regret bounds and non-trivial sample path-regret bounds under the high probability regime. 

Possible extensions of this work include: \emph{(i)} designing anytime policies when $T$ is unknown, \emph{(ii)} considering the setting where the rate of growth of the experts is random, i.e., the environment samples a random number of points in each round, and \emph{(iii)} studying the setting where the new experts are approximate clones of the parent experts instead of being perfect clones. Further, the setting of stochastically partitioning experts with stochastic losses can also be explored. 
%Obtaining tighter sample-path regret guarantees for $d>1$ remains an open problem.


% \section{Future Work}
% \begin{itemize}
% \item \textbf{What if $\mathbb{B}$ is not a hyper-cube?}
% \item \textbf{Uncountably Infinite Experts}: Using partitions as experts is a countably infinite expert setting. We consider an uncountably infinite expert setting where the points are experts. Only the losses of the points drawn so far are revealed by the environment (but not loss per partition). The learner assigns the losses of the points in some way drawn to the points in partitions. For example, the cumulative loss of a point in a partition is approximated by the cumulative loss of the nearest point revealed.
% \item What if the losses are random, not adversarial?
% \end{itemize}

