Ballooning Multi-Armed Bandits
Ganesh Ghalme, Swapnil Dhamal, Shweta Jain, Sujit Gujar, Y. Narahari

TL;DR
This paper introduces Ballooning Multi-Armed Bandits, a new model where arms grow over time, and proposes algorithms with sub-linear regret under certain arrival distributions, supported by theoretical analysis and simulations.
Contribution
The paper defines the novel BL-MAB model, analyzes regret behavior, and proposes algorithms achieving sub-linear regret based on arm arrival distributions.
Findings
Existing algorithms result in linear regret in BL-MAB.
Sub-linear regret is achievable if the best arm arrives early.
Proposed algorithm adapts exploration based on arrival distribution.
Abstract
In this paper, we introduce Ballooning Multi-Armed Bandits (BL-MAB), a novel extension of the classical stochastic MAB model. In the BL-MAB model, the set of available arms grows (or balloons) over time. In contrast to the classical MAB setting where the regret is computed with respect to the best arm overall, the regret in a BL-MAB setting is computed with respect to the best available arm at each time. We first observe that the existing stochastic MAB algorithms result in linear regret for the BL-MAB model. We prove that, if the best arm is equally likely to arrive at any time instant, a sub-linear regret cannot be achieved. Next, we show that if the best arm is more likely to arrive in the early rounds, one can achieve sub-linear regret. Our proposed algorithm determines (1) the fraction of the time horizon for which the newly arriving arms should be explored and (2) the sequence of…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Smart Grid Energy Management · Reinforcement Learning in Robotics
