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100
Theory and applications of Robust Optimization
, 2007
"... In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most pr ..."
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Cited by 100 (14 self)
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In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multistage decisionmaking problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.
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 64 (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.
An Adaptive Algorithm for Selecting Profitable Keywords for SearchBased Advertising Services
 In EC ’06: Proceedings of the 7th ACM conference on Electronic commerce
, 2006
"... Increases in online searches have spurred the growth of searchbased advertising services offered by search engines, enabling companies to promote their products to consumers based on search queries. With millions of available keywords whose clickthru rates and profits are highly uncertain, identify ..."
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Cited by 61 (0 self)
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Increases in online searches have spurred the growth of searchbased advertising services offered by search engines, enabling companies to promote their products to consumers based on search queries. With millions of available keywords whose clickthru rates and profits are highly uncertain, identifying the most profitable set of keywords becomes challenging. We formulate a stylized model of keyword selection in searchbased advertising services. Assuming known profits and unknown clickthru rates, we develop an approximate adaptive algorithm that prioritizes keywords based on a prefix ordering – sorting of keywords in a descending order of expectedprofittocost ratio (or “bangperbuck”). We show that the average expected profit generated by our algorithm converges to nearoptimal profits, with the convergence rate that is independent of the number of keywords and scales gracefully with the problem’s parameters. By leveraging the special structure of our problem, our algorithm trades off bias with faster convergence rate, converging very quickly but with only nearoptimal profit in the limit. Extensive numerical simulations show that when the number of keywords is large, our algorithm outperforms existing methods, increasing profits by about 20 % in as little as 40 periods. We also extend our algorithm to the setting when both the clickthru rates and the expected profits are unknown. 1
A knapsack secretary problem with applications
 In APPROX ’07
, 2007
"... Fellowship. Portions of this work were completed while the author was a postdoctoral ..."
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Cited by 53 (5 self)
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Fellowship. Portions of this work were completed while the author was a postdoctoral
Universal approximations for TSP, Steiner tree, and set cover
 In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC’05
, 2005
"... We introduce a notion of universality in the context of optimization problems with partial information. Universality is a framework for dealing with uncertainty by guaranteeing a certain quality of goodness for all possible completions of the partial information set. Universal variants of optimizati ..."
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Cited by 36 (3 self)
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We introduce a notion of universality in the context of optimization problems with partial information. Universality is a framework for dealing with uncertainty by guaranteeing a certain quality of goodness for all possible completions of the partial information set. Universal variants of optimization problems can be defined that are both natural and wellmotivated. We consider universal versions of three classical problems: TSP, Steiner Tree and Set Cover. We present a polynomialtime algorithm to find a universal tour on a given metric space over vertices such that for any subset of the vertices, the subtour induced by the subset is within of an optimal tour for the subset. Similarly, we show that given a metric space over vertices and a root vertex, we can find a universal spanning tree such that for any subset of vertices containing the root, the subtree induced by the subset is within of an optimal Steiner tree for the subset. Our algorithms rely on a new notion of sparse partitions, that may be of independent interest. For the special case of doubling metrics, which includes both constantdimensional Euclidean and growthrestricted metrics, our algorithms achieve an upper bound. We complement our results for the universal Steiner tree problem with a lower bound of that holds even for vertices on the plane. We also show that a slight generalization of the universal Steiner Tree problem is coNPhard and present nearly tight upper and lower bounds for a universal version
Online Auctions and Generalized Secretary Problems
"... We present generalized secretary problems as a framework for online auctions. Elements, such as potential employees or customers, arrive one by one online. After observing the value derived from an element, but without knowing the values of future elements, the algorithm has to make an irrevocable d ..."
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Cited by 35 (0 self)
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We present generalized secretary problems as a framework for online auctions. Elements, such as potential employees or customers, arrive one by one online. After observing the value derived from an element, but without knowing the values of future elements, the algorithm has to make an irrevocable decision whether to retain the element as part of a solution, or reject it. The way in which the secretary framework differs from traditional online algorithms is that the elements arrive in uniformly random order. Many natural online auction scenarios can be cast as generalized secretary problems, by imposing natural restrictions on the feasible sets. For many such settings, we present surprisingly strong constant factor guarantees on the expected value of solutions obtained by online algorithms. The framework is also easily augmented to take into account timediscounted revenue and incentive compatibility. We give an overview of recent results and future research directions.
Oblivious network design
"... Consider the following network design problem: given anetwork G = (V, E), sourcesink pairs {si, ti} arrive anddesire to send a unit of flow between themselves. The cost of the routing is this: if edge e carries a total of fe flow (from allthe terminal pairs), the cost is given by P e `(fe), where ..."
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Cited by 35 (7 self)
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Consider the following network design problem: given anetwork G = (V, E), sourcesink pairs {si, ti} arrive anddesire to send a unit of flow between themselves. The cost of the routing is this: if edge e carries a total of fe flow (from allthe terminal pairs), the cost is given by P e `(fe), where ` issome concave cost function; the goal is to minimize the total cost incurred. However, we want the routing to be oblivious:when terminal pair { si, ti} makes its routing decisions, itdoes not know the current flow on the edges of the network, nor the identity of the other pairs in the system. Moreover,it does not even know the identity of the function `, merelyknowing that ` is a concave function of the total flow on theedge. How should it (obliviously) route its one unit of flow? Can we get competitive algorithms for this problem?In this paper, we develop a framework to model oblivious network design problems (of which the above problemis a special case), and give algorithms with polylogarithmic competitive ratio for problems in this framework (and hencefor this problem). Abstractly, given a problem like the one above, the solution is a multicommodity flow producing a&quot;load &quot; on each edge of Le = `(f1(e), f2(e),..., fk(e)),and the total cost is given by an &quot;aggregation function&quot; agg(Le1,..., Lem) of the loads of all edges. Our goal is todevelop oblivious algorithms that approximately minimize the total cost of the routing, knowing the aggregation function agg, but merely knowing that ` lies in some class C, andhaving no other information about the current state of the network. Hence we want algorithms that are simultaneously&quot;functionoblivious &quot; as well as &quot;trafficoblivious&quot;. The aggregation functions we consider are the max andP objective functions, which correspond to the wellknown measures of congestion and total cost of a network; in thispaper, we prove the following: * If the aggregation function is P, we give an oblivious algorithm with
Approximation algorithms for budgeted learning problems
 In Proc. ACM Symp. on Theory of Computing
, 2007
"... We present the first approximation algorithms for a large class of budgeted learning problems. One classic example of the above is the budgeted multiarmed bandit problem. In this problem each arm of the bandit has an unknown reward distribution on which a prior is specified as input. The knowledge ..."
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Cited by 31 (8 self)
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We present the first approximation algorithms for a large class of budgeted learning problems. One classic example of the above is the budgeted multiarmed bandit problem. In this problem each arm of the bandit has an unknown reward distribution on which a prior is specified as input. The knowledge about the underlying distribution can be refined in the exploration phase by playing the arm and observing the rewards. However, there is a budget on the total number of plays allowed during exploration. After this exploration phase, the arm with the highest (posterior) expected reward is chosen for exploitation. The goal is to design the adaptive exploration phase subject to a budget constraint on the number of plays, in order to maximize the expected reward of the arm chosen for exploitation. While this problem is reasonably well understood in the infinite horizon setting or regret bounds, the budgeted version of the problem is NPHard. For this problem, and several generalizations, we provide approximate policies that achieve a reward within constant factor of the reward optimal policy. Our algorithms use a novel linear program rounding technique based on stochastic packing.
Toward a model for backtracking and dynamic programming
 Comput. Compl
"... We propose a model called priority branching trees (pBT) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. ..."
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Cited by 27 (7 self)
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We propose a model called priority branching trees (pBT) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and Satisfiability.
Approximation algorithms for 2stage stochastic optimization problems
 SIGACT News
, 2006
"... Abstract. Stochastic optimization is a leading approach to model optimization problems in which there is uncertainty in the input data, whether from measurement noise or an inability to know the future. In this survey, we outline some recent progress in the design of polynomialtime algorithms with p ..."
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Cited by 23 (1 self)
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Abstract. Stochastic optimization is a leading approach to model optimization problems in which there is uncertainty in the input data, whether from measurement noise or an inability to know the future. In this survey, we outline some recent progress in the design of polynomialtime algorithms with performance guarantees on the quality of the solutions found for an important class of stochastic programming problems — 2stage problems with recourse. In particular, we show that for a number of concrete problems, algorithmic approaches that have been applied for their deterministic analogues are also effective in this more challenging domain. More specifically, this work highlights the role of tools from linear programming, rounding techniques, primaldual algorithms, and the role of randomization more generally. 1