In this research, we examine dynamic environments and choose dynamic regret and adaptive regret to measure the performance.

In the introduction we discuss exact oracles for simplicity, but our results account for inexactness. Our results hold for any weighted Euclidean (semi)norm, i.e.,

We consider the problem of online learning and its application to solving minimax games. For the online learning problem, Follow the Perturbed Leader (FTPL) is a widely studied algorithm which enjoys the optimal $O(T^{1/2})$ \emph{worst case} regret guarantee for both convex and nonconvex losses. In this work, we show that when the sequence of loss functions is \emph{predictable}, a simple modification of FTPL which incorporates optimism can achieve better regret guarantees, while retaining the optimal worst-case regret guarantee for unpredictable sequences. A key challenge in obtaining these tighter regret bounds is the stochasticity and optimism in the algorithm, which requires different analysis techniques than those commonly used in the analysis of FTPL. The key ingredient we utilize in our analysis is the dual view of perturbation as regularization.

Neural Information Processing Systems http://nips.cc/

In this research, we examine dynamic environments and choose dynamic regret and adaptive regret to measure the performance.

In contrast to previous work on this learning model, we consider scenarios in which the family of groups is too large to explicitly enumerate, and hence we seek algorithms that only access groups via an optimization oracle.