On distributed submodular maximization with limited information

Gharesifard, Bahman; Smith, Stephen L.

doi:10.1109/acc.2016.7525053

Cited by 25 publications

(55 citation statements)

References 26 publications

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“…This paper extends methods for distributed planning to target tracking problems, presents analysis that accounts for common approximations, and applies these methods to multirobot planning in a simulated target tracking scenario. 2 1) Distributed planning for target tracking: Although sequential planners generally require computation time that is at least proportional to the number of robots, recent works on distributed optimization introduced methods that can reduce the number of sequential steps [25,26]. Our prior works built on these to develop planners based on Randomized Sequential Partitions 3 (RSP) that run in constant numbers of steps, independent of the number of robots [16,18].…”

Section: A Contributionsmentioning

confidence: 99%

“…. , i − 1} of these decisions, which induces a directed acyclic graph with edges (j, i) for each robot j ∈ N in i whose decision i accesses while planning [25,26]. In a sense, the robots ignore decisions by N in i = {1, .…”

Section: B Cost Of Distributed Planning On Directed Acyclic Graphsmentioning

confidence: 99%

“…Remark 1: Our prior work [16] relies on g(A; B|X) increasing monotonically in X to state g(A; B|X) ≥ g(A; B). To unify this result with (25), we state that each produces a lower bound on g(A; B|X) as a function of A and B.…”

Section: B Bounding the Cost Of Distributed Planning For Target Track...mentioning

confidence: 99%

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Scalable Distributed Planning for Multi-Robot, Multi-Target Tracking

Corah¹,

Michael²

2021

Preprint

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In multi-robot multi-target tracking, robots coordinate to monitor groups of targets moving about an environment. We approach planning for such scenarios by formulating a receding-horizon, multi-robot sensing problem with a mutual information objective. Such problems are NP-Hard in general. Yet, our objective is submodular which enables certain greedy planners to guarantee constant-factor suboptimality. However, these greedy planners require robots to plan their actions in sequence, one robot at a time, so planning time is at least proportional to the number of robots. Solving these problems becomes intractable for large teams, even for distributed implementations. Our prior work proposed a distributed planner (RSP) which reduces this number of sequential steps to a constant, even for large numbers of robots, by allowing robots to plan in parallel while ignoring some of each others' decisions. Although that analysis is not applicable to target tracking, we prove a similar guarantee, that RSP planning approaches performance guarantees for fully sequential planners, by employing a novel bound which takes advantage of the independence of target motions to quantify effective redundancy between robots' observations and actions. Further, we present analysis that explicitly accounts for features of practical implementations including approximations to the objective and anytime planning. Simulation results-available via open source release-for target tracking with ranging sensors demonstrate that our planners consistently approach the performance of sequential planning (in terms of position uncertainty) given only 2-8 planning steps and for as many as 96 robots with a 24x reduction in the number of sequential steps in planning. Thus, this work makes planning for multi-robot target tracking tractable at much larger scales than before, for practical planners and general tracking problems.

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Section: A Contributionsmentioning

confidence: 99%

Section: B Cost Of Distributed Planning On Directed Acyclic Graphsmentioning

confidence: 99%

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Scalable Distributed Planning for Multi-Robot, Multi-Target Tracking

Corah¹,

Michael²

2021

Preprint

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“…In these scenarios, a team of agents are attempting to maximize a submodular objective function collaboratively. Each agent has access to their own set of actions and can observe a limited number of decisions made by other agents [25], [10], [26], [27], [28]. In contrast, we consider the case where each decision-maker has limited access to the function f itself.…”

Section: Introductionmentioning

confidence: 99%

Submodular Maximization with Limited Function Access

Downie¹,

Smith²,

Smith³

2022

Preprint

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We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decisionmaker can observe only pairwise information, i.e., can evaluate the objective function on sets of size two. We begin with a negative result that no algorithm using only k-wise information can guarantee performance better than k/n. We present two algorithms that utilize only pairwise information about the function and characterize their performance relative to the optimal, which depends on the curvature of the submodular function. Additionally, if the submodular function possess a property called supermodularity of conditioning, then we can provide a method to bound the performance based purely on pairwise information. The proposed algorithms offer significant computational speedups over a traditional greedy strategy. A by-product of our study is the introduction of two new notions of curvature, the k-Marginal Curvature and the k-Cardinality Curvature. Finally, we present experiments highlighting the performance of our proposed algorithms in terms of approximation and time complexity.

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“…The greedy algorithm cannot be directly implemented in the scenarios where the robots can only communicate locally due to a limited communication range. To address the issue of local communication, some decentralized versions of the greedy algorithm were designed, where only neighboring information is utilized to choose actions for the robots for optimizing submodular objectives [11], [12], [13], [14]. However, these algorithms either assume a connected communication graph [11], [12] or typically have a worse suboptimality bound than that of the greedy algorithm [10] in the scenarios with limited communication [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Graph Neural Networks for Decentralized Multi-Robot Submodular Action Selection

Zhou¹,

Sharma²,

Li³

et al. 2021

Preprint

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In this paper, we develop a learning-based approach for decentralized submodular maximization. We focus on applications where robots are required to jointly select actions, e.g., motion primitives, to maximize team submodular objectives with local communications only. Such applications are essential for large-scale multi-robot coordination such as multi-robot motion planning for area coverage, environment exploration, and target tracking. But the current decentralized submodular maximization algorithms either require assumptions on the inter-robot communication or lose some suboptimal guarantees. In this work, we propose a general-purpose learning architecture towards submodular maximization at scale, with decentralized communications. Particularly, our learning architecture leverages a graph neural network (GNN) to capture local interactions of the robots and learns decentralized decision-making for the robots. We train the learning model by imitating an expert solution and implement the resulting model for decentralized action selection involving local observations and communications only. We demonstrate the performance of our GNN-based learning approach in a scenario of active target coverage with large networks of robots. The simulation results show our approach nearly matches the coverage performance of the expert algorithm, and yet runs several orders faster with more than 30 robots. The results also exhibit our approach's generalization capability in previously unseen scenarios, e.g., larger environments and larger networks of robots.

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On distributed submodular maximization with limited information

Cited by 25 publications

References 26 publications

Scalable Distributed Planning for Multi-Robot, Multi-Target Tracking

Scalable Distributed Planning for Multi-Robot, Multi-Target Tracking

Submodular Maximization with Limited Function Access

Graph Neural Networks for Decentralized Multi-Robot Submodular Action Selection

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