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14
Adaptive submodularity: Theory and applications in active learning and stochastic optimization
 J. Artificial Intelligence Research
, 2011
"... Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive subm ..."
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Cited by 70 (15 self)
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Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse AI applications including management of sensing resources, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations. 1.
Lagrangian relaxation techniques for scalable spatial conservation planning
 In Twentysixth AAAI Conference on Artificial Intelligence
, 2012
"... We address the problem of spatial conservation planning in which the goal is to maximize the expected spread of cascades of an endangered species by strategically purchasing land parcels within a given budget. This problem can be solved by standard integer programming methods using the sample avera ..."
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Cited by 12 (7 self)
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We address the problem of spatial conservation planning in which the goal is to maximize the expected spread of cascades of an endangered species by strategically purchasing land parcels within a given budget. This problem can be solved by standard integer programming methods using the sample average approximation (SAA) scheme. Our main contribution lies in exploiting the separable structure present in this problem and using Lagrangian relaxation techniques to gain scalability over the flat representation. We also generalize the approach to allow the application of the SAA scheme to a range of stochastic optimization problems. Our iterative approach is highly efficient in terms of space requirements and it provides an upper bound over the optimal solution at each iteration. We apply our approach to the Redcockaded
Nearoptimal Batch Mode Active Learning and Adaptive Submodular Optimization
"... Active learning can lead to a dramatic reduction in labeling effort. However, in many practical implementations (such as crowdsourcing, surveys, highthroughput experimental design), it is preferable to query labels for batches of examples to be labelled in parallel. While several heuristics have be ..."
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Cited by 12 (1 self)
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Active learning can lead to a dramatic reduction in labeling effort. However, in many practical implementations (such as crowdsourcing, surveys, highthroughput experimental design), it is preferable to query labels for batches of examples to be labelled in parallel. While several heuristics have been proposed for batchmode active learning, little is known about their theoretical performance. We consider batch mode active learning and more general informationparallel stochastic optimization problems that exhibit adaptive submodularity, a natural diminishing returns condition. We prove that for such problems, a simple greedy strategy is competitive with the optimal batchmode policy. In some cases, surprisingly, the use of batches incurs competitively low cost, even when compared to a fully sequential strategy. We demonstrate the effectiveness of our approach on batchmode active learning tasks, where it outperforms the state of the art, as well as the novel problem of multistage influence maximization in social networks. 1.
Rounded Dynamic Programming for TreeStructured Stochastic Network Design
"... We develop a fast approximation algorithm called rounded dynamic programming (RDP) for stochastic network design problems on directed trees. The underlying model describes phenomena that spread away from the root of a tree, for example, the spread of influence in a hierarchical organization or fish ..."
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Cited by 5 (3 self)
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We develop a fast approximation algorithm called rounded dynamic programming (RDP) for stochastic network design problems on directed trees. The underlying model describes phenomena that spread away from the root of a tree, for example, the spread of influence in a hierarchical organization or fish in a river network. Actions can be taken to intervene in the network—for some cost—to increase the probability of propagation along an edge. Our algorithm selects a set of actions to maximize the overall spread in the network under a limited budget. We prove that the algorithm is a fully polynomialtime approximation scheme (FPTAS), that is, it finds (1−)optimal solutions in time polynomial in the input size and 1/. We apply the algorithm to the problem of allocating funds efficiently to remove barriers in a river network so fish can reach greater portions of their native range. Our experiments show that the algorithm is able to produce nearoptimal solutions much faster than an existing technique.
Scheduling Conservation Designs via Network Cascade Optimization
"... We introduce the problem of scheduling land purchases to conserve an endangered species in a way that achieves maximum population spread but delays purchases as long as possible, so that conservation planners retain maximum flexibility and use available budgets in the most efficient way. We devel ..."
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Cited by 4 (4 self)
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We introduce the problem of scheduling land purchases to conserve an endangered species in a way that achieves maximum population spread but delays purchases as long as possible, so that conservation planners retain maximum flexibility and use available budgets in the most efficient way. We develop the problem formally as a stochastic optimization problem over a network cascade model describing the population spread, and present a solution approach that reduces the stochastic problem to a novel variant of a Steiner tree problem. We give a primaldual algorithm for the problem that computes both a feasible solution and a bound on the quality of an optimal solution. Our experiments, using actual conservation data and a standard diffusion model, show that the approach produces near optimal results and is much more scalable than more generic offtheshelf optimizers. 1
Dynamic Resource Allocation for Optimizing Population Diffusion
"... This paper addresses adaptive conservation planning, where the objective is to maximize the population spread of a species by allocating limited resources over time to conserve land parcels. This problem is characterized by having highly stochastic exogenous events (population spread), a large a ..."
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Cited by 3 (1 self)
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This paper addresses adaptive conservation planning, where the objective is to maximize the population spread of a species by allocating limited resources over time to conserve land parcels. This problem is characterized by having highly stochastic exogenous events (population spread), a large action branching factor (number of allocation options) and state space, and the need to reason about numeric resources. Together these characteristics render most existing AI planning techniques ineffective. The main contribution of this paper is to design and evaluate an online planner for this problem based on Hindsight Optimization (HOP), a technique that has shown promise in other stochastic planning problems. Unfortunately, standard implementations of HOP scale linearly with the number of actions in a domain, which is not feasible for conservation problems such as ours. Thus, we develop a new approach for computing HOP policies based on mixedinteger programming and dual decomposition. Our experiments on synthetic and realworld scenarios show that this approach is effective and scalable compared to existing alternatives. 1
Parameter Learning for Latent Network Diffusion
"... Diffusion processes in networks are increasingly used to model dynamic phenomena such as the spread of information, wildlife, or social influence. Our work addresses the problem of learning the underlying parameters that govern such a diffusion process by observing the time at which nodes become act ..."
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Cited by 2 (1 self)
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Diffusion processes in networks are increasingly used to model dynamic phenomena such as the spread of information, wildlife, or social influence. Our work addresses the problem of learning the underlying parameters that govern such a diffusion process by observing the time at which nodes become active. A key advantage of our approach is that, unlike previous work, it can tolerate missing observations for some nodes in the diffusion process. Having incomplete observations is characteristic of offline networks used to model the spread of wildlife. We develop an EM algorithm to address parameter learning in such settings. Since both the E and M steps are computationally challenging, we employ a number of optimization methods such as nonlinear and differenceofconvex programming to address these challenges. Evaluation of the approach on the Redcockaded Woodpecker conservation problem shows that it is highly robust and accurately learns parameters in various settings, even with more than 80 % missing data. 1
Collective diffusion over networks: Models and inference
 In International Conference on Uncertainty in Artificial Intelligence
, 2013
"... Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility pattern, the observed data often consists of only aggreg ..."
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Cited by 2 (2 self)
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Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility pattern, the observed data often consists of only aggregate information. In this work, we present new models that generalize standard diffusion processes to such collective settings. We also present optimization based techniques that can accurately learn the underlying dynamics of the given contagion process, including the hidden network structure, by only observing the time a node becomes active and the associated aggregate information. Empirically, our technique is highly robust and accurately learns network structure with more than 90 % recall and precision. Results on realworld flu spread data in the US confirm that our technique can also accurately model infectious disease spread. 1
Scheduling conservation designs for maximum flexibility via network cascade optimization
 Journal of Artificial Intelligence Research
"... One approach to conserving endangered species is to purchase and protect a set of land parcels in a way that maximizes the expected future population spread. Unfortunately, an ideal set of parcels may have a cost that is beyond the immediate budget constraints and must thus be purchased incrementall ..."
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Cited by 1 (1 self)
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One approach to conserving endangered species is to purchase and protect a set of land parcels in a way that maximizes the expected future population spread. Unfortunately, an ideal set of parcels may have a cost that is beyond the immediate budget constraints and must thus be purchased incrementally. This raises the challenge of deciding how to schedule the parcel purchases in a way that maximizes the flexibility of budget usage while keeping population spread loss in control. In this paper, we introduce a formulation of this scheduling problem that does not rely on knowing the future budgets of an organization. In particular, we consider scheduling purchases in a way that achieves a population spread no less than desired but delays purchases as long as possible. Such schedules offer conservation planners maximum flexibility and use available budgets in the most efficient way. We develop the problem formally as a stochastic optimization problem over a network cascade model describing a commonly used model of population spread. Our solution approach is based on reducing the stochastic problem to a novel variant of the directed Steiner tree problem, which we call the setweighted directed Steiner graph problem. We show that this problem is computationally hard, motivating the development of a primaldual algorithm for the problem that computes both a feasible solution and a bound on the quality of an optimal solution. We evaluate the approach on both real and synthetic conservation data with a standard population spread model. The algorithm is shown to produce near optimal results and is much more scalable than more generic offtheshelf optimizers. Finally, we evaluate a variant of the algorithm to explore the tradeoffs between budget savings and population growth. 1.
Stochastic Network Design for River Networks
"... Stochastic network design techniques can be used effectively to solve a wide range of planning problems in ecological sustainability. We propose a novel approximate algorithm based on the sample average approximation (SAA) and mixed integer programming (MIP) to efficiently address the problem of us ..."
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Cited by 1 (1 self)
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Stochastic network design techniques can be used effectively to solve a wide range of planning problems in ecological sustainability. We propose a novel approximate algorithm based on the sample average approximation (SAA) and mixed integer programming (MIP) to efficiently address the problem of using a limited budget to remove instream barriers, which prevent fish from accessing their natural habitat. In comparison with a dynamic programming (DP) benchmark algorithm, the advantage of our algorithm is the ability to produce a near optimal solution much faster, particularly when the budget is large and the DP based algorithm becomes intractable. Furthermore, while the DP based algorithm can only solve treestructured stream networks, our algorithm is applicable to networks with a more general directed acyclic graph structure. 1