Online Distributed Sensor Selection

A key challenge in deploying sensor networks for realworld applications such as environmental monitoring [19], building automation [25] and others is to decide when to activate the sensors in order to obtain the most useful information from the network (e.g., accurate predictions at unobserved locations) and to minimize power consumption. This sensor selection problem has received considerable attention [1,32,10], and algorithms with performance guarantees have been developed [1,16]. However, many of the existing approaches make simplifying assumptions. Many approaches assume (1) that the sensors can perfectly observe a particular sensing region, and nothing outside the region [1]. This assumption does not allow us to model settings where multiple noisy sensors can help each other obtain better predictions. There are also approaches that base their notion of utility on more detailed models, such as improvement in prediction accuracy w.r.t. some statistical model [10] or detection performance [18]. However, most of these approaches make two crucial assumptions: (2) The model, upon which the optimization is based, is known in advance (e.g., based on domain knowledge or data from a pilot deployment) and (3), a centralized optimization selects the sensors (i.e., some centralized processor selects the sensors which obtain highest utility w.r.t. the model). We are not aware of any approach that simultaneously addresses the three main challenges (1), (2) and (3) above and still provides theoretical guarantees.

In this paper, we develop an efficient algorithm, called Distributed Online Greedy (DOG), which addresses these three central challenges. Prior work [17] has shown that many sensing tasks satisfy an intuitive diminishing returns property, submodularity, which states that activating a new sensor helps more if few sensors have been activated so far, and less if many sensors have already been activated. Our algorithm applies to any setting where the true objective is submodular [23], thus capturing a variety of realistic sensor models. Secondly, our algorithm does not require the model to be specified in advance: it learns to optimize the objective function in an online manner. Lastly, the algorithm is distributed; the sensors decide whether to activate themselves based on local information. We analyze our algorithm in the no-regret model, proving convergence properties similar to the best bounds for any centralized solution.

A bandit approach toward sensor selection. At the heart of our approach is a novel distributed algorithm for multi-armed bandit (MAB) problems. In the classical multiarmed bandit [24] setting, we picture a slot machine with multiple arms, where each arm generates a random payoff with unknown mean. Our goal is to devise a strategy for pulling arms to maximize the total reward accrued. The difference between the optimal arm’s payoff and the obtained payoff is called the regret. Known algorithms can achieve average per-round regret of O( √ n log n/ √ T ) where n is the number of arms, and T the number of rounds (see e.g. the survey of [13]). Suppose we would like to, at every time step, select k sensors. The sensor selection problem can then be cast as a multiarmed bandit problem, where there is one arm for each possible set of k sensors, and the payoff is the accrued utility for the selected set. Since the number of possible sets, and thus the number of arms, is exponentially large, the resulting regret bound is O(n k/2 √ log n/ √ T ), i.e., exponential in k. However, when the utility function is submodular, the payoffs of these arms are correlated. Recent results [28] show that this correlation due to submodularity can be exploited by reducing the n k -armed bandit problem to k separate n-armed bandit problems, with only a bounded loss in performance. Existing bandit algorithms, such as the widely used EXP3 algorithm [2], are centralized in nature. Consequently, the key challenge in distributed online submodular sensing is how to devise a distributed bandit algorithm. In Sec. 4 and 5, we develop a distributed variant of EXP3 using novel algorithms to sample from and update a probability distribution in a distributed way. Roughly, we develop a scheme where each sensor maintains its own weight, and activates itself independently from all other sensors purely depending on this weight.

Observation specific selection. A shortcoming of centralized sensor selection is that the individual sensors’ current measurements are not considered in the selection process. In many applications, obtaining sensor measurements is less costly than transmitting the measurements across the network. For example, cell phones used in participatory sensing [5] can inexpensively obtain measurements on a regular basis, but it is expensive to constantly communicate measurements over the network. In Sec. 6, we extend our distributed selection algorithm to activate sensors depending on their observations, and analyze the

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