Abstract—We consider two variants of the standard multi-armed bandit problem, namely, the multi-armed bandit prob-lem with transition costs and the multi-armed bandit problem on graphs. We develop block allocation algorithms for these problems that achieve an expected cumulative regret that is uniformly dominated by a logarithmic function of time, and an expected cumulative number of transitions from one arm to another arm uniformly dominated by a double-logarithmic function of time. We observe that the multi-armed bandit prob-lem with transition costs and the associated block allocation algorithm capture the key features of popular animal foraging models in literature. I.

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The emergence of mobile and fixed sensor networks operating at different modalities, mobility, and coverage has enabled access to an unprecedented amount of information. In a variety of complex and information rich systems, this information is processed by a human operator [1, 2]. The inherent inability of humans to handle the plethora of available information has detrimental effects on their performance and may lead to dire consequences [3]. To alleviate this loss in performance of the human operator, the recent National Robotic Initiative [4] emphasizes collaboration of humans with robotic partners, and envisions a symbiotic co-robot that facilitates an efficient interaction of the human operator with the automaton. An efficient co-robotic partner will enable a better interaction between the automaton and the operator by exploiting the oper-ator’s strengths while taking into account their inefficiencies,

Abstract—We study collective decision-making in a model of human groups, with network interactions, performing two alternative choice tasks. We focus on the speed-accuracy tradeoff, i.e., the tradeoff between a quick decision and a reliable decision, for individuals in the network. We model the evidence aggrega-tion process across the network using a coupled drift diffusion model (DDM) and consider the free response paradigm in which individuals take their time to make the decision. We develop reduced DDMs as decoupled approximations to the coupled DDM and characterize their efficiency. We determine high probability bounds on the error rate and the expected decision time for the reduced DDM. We show the effect of the decision-maker’s location in the network on their decision-making performance under several threshold selection criteria. Finally, we extend the coupled DDM to the coupled Ornstein-Uhlenbeck model for decision-making in two alternative choice tasks with recency effects, and to the coupled race model for decision-making in multiple alternative choice tasks. Index Terms—Distributed decision-making, coupled drift-diffusion model, decision time, error rate, coupled Orhstein-Uhlenbeck model, coupled race model, distributed sequential hypothesis testing I.