ﻻ يوجد ملخص باللغة العربية
We propose an algorithm for stochastic and adversarial multiarmed bandits with switching costs, where the algorithm pays a price $lambda$ every time it switches the arm being played. Our algorithm is based on adaptation of the Tsallis-INF algorithm of Zimmert and Seldin (2021) and requires no prior knowledge of the regime or time horizon. In the oblivious adversarial setting it achieves the minimax optimal regret bound of $Obig((lambda K)^{1/3}T^{2/3} + sqrt{KT}big)$, where $T$ is the time horizon and $K$ is the number of arms. In the stochastically constrained adversarial regime, which includes the stochastic regime as a special case, it achieves a regret bound of $Oleft(big((lambda K)^{2/3} T^{1/3} + ln Tbig)sum_{i eq i^*} Delta_i^{-1}right)$, where $Delta_i$ are the suboptimality gaps and $i^*$ is a unique optimal arm. In the special case of $lambda = 0$ (no switching costs), both bounds are minimax optimal within constants. We also explore variants of the problem, where switching cost is allowed to change over time. We provide experimental evaluation showing competitiveness of our algorithm with the relevant baselines in the stochastic, stochastically constrained adversarial, and adversarial regimes with fixed switching cost.
We derive an algorithm that achieves the optimal (within constants) pseudo-regret in both adversarial and stochastic multi-armed bandits without prior knowledge of the regime and time horizon. The algorithm is based on online mirror descent (OMD) wit
We study the adversarial multi-armed bandit problem where partial observations are available and where, in addition to the loss incurred for each action, a emph{switching cost} is incurred for shifting to a new action. All previously known results in
We propose a new algorithm for adversarial multi-armed bandits with unrestricted delays. The algorithm is based on a novel hybrid regularizer applied in the Follow the Regularized Leader (FTRL) framework. It achieves $mathcal{O}(sqrt{kn}+sqrt{Dlog(k)
We derive improved regret bounds for the Tsallis-INF algorithm of Zimmert and Seldin (2021). We show that in adversarial regimes with a $(Delta,C,T)$ self-bounding constraint the algorithm achieves $mathcal{O}left(left(sum_{i eq i^*} frac{1}{Delta_i}
We develop the first general semi-bandit algorithm that simultaneously achieves $mathcal{O}(log T)$ regret for stochastic environments and $mathcal{O}(sqrt{T})$ regret for adversarial environments without knowledge of the regime or the number of roun