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27
Beyond equilibria: Mechanisms for repeated combinatorial auctions
, 2009
"... We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of thei ..."
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We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of their bidding strategies, or apply shortsighted bestresponse strategies. We ask: when can a blackbox approximation algorithm for the base auction problem be converted into a mechanism that approximately preserves the original algorithm’s approximation factor on average over many iterations? We present a general reduction for a broad class of algorithms when agents minimize external regret. We also present a mechanism for the combinatorial auction problem that attains an O (√m) approximation on average when agents apply bestresponse dynamics.
Using Online Algorithms to Solve NPHard Problems More Efficiently in Practice
, 2007
"... as representing the official policies of the U.S. Government. ..."
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as representing the official policies of the U.S. Government.
Combinatorial multiarmed bandit and its extension to probabilistically triggered arms.
 Journal of Machine Learning Research,
, 2016
"... Abstract We define a general framework for a large class of combinatorial multiarmed bandit (CMAB) problems, where subsets of base arms with unknown distributions form super arms. In each round, a super arm is played and the base arms contained in the super arm are played and their outcomes are ob ..."
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Abstract We define a general framework for a large class of combinatorial multiarmed bandit (CMAB) problems, where subsets of base arms with unknown distributions form super arms. In each round, a super arm is played and the base arms contained in the super arm are played and their outcomes are observed. We further consider the extension in which more base arms could be probabilistically triggered based on the outcomes of already triggered arms. The reward of the super arm depends on the outcomes of all played arms, and it only needs to satisfy two mild assumptions, which allow a large class of nonlinear reward instances. We assume the availability of an offline (α, β)approximation oracle that takes the means of the outcome distributions of arms and outputs a super arm that with probability β generates an α fraction of the optimal expected reward. The objective of an online learning algorithm for CMAB is to minimize (α, β)approximation regret, which is the difference in total expected reward between the αβ fraction of expected reward when always playing the optimal super arm, and the expected reward of playing super arms according to the algorithm. We provide CUCB algorithm that achieves O(log n) distributiondependent regret, where n is the number of rounds played, and we further provide distributionindependent bounds for a large class of reward functions. Our regret analysis is tight in that it matches the bound of UCB1 algorithm (up to a constant factor) for the classical MAB problem, and it significantly improves the regret bound in an earlier paper on combinatorial bandits * . A preliminary version of this paper has appeared in ICML
Online Submodular Minimization for Combinatorial Structures
"... Most results for online decision problems with structured concepts, such as trees or cuts, assume linear costs. In many settings, however, nonlinear costs are more realistic. Owing to their nonseparability, these lead to much harder optimization problems. Going beyond linearity, we address online a ..."
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Cited by 3 (2 self)
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Most results for online decision problems with structured concepts, such as trees or cuts, assume linear costs. In many settings, however, nonlinear costs are more realistic. Owing to their nonseparability, these lead to much harder optimization problems. Going beyond linearity, we address online approximation algorithms for structured concepts that allow the cost to be submodular, i.e., nonseparable. In particular, we show regret bounds for three Hannanconsistent strategies that capture different settings. Our results also tighten a regret bound for unconstrained online submodular minimization. 1.
Regret Minimization and Job Scheduling
"... Abstract. Regret minimization has proven to be a very powerful tool in both computational learning theory and online algorithms. Regret minimization algorithms can guarantee, for a single decision maker, a near optimal behavior under fairly adversarial assumptions. I will discuss a recent extensions ..."
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Abstract. Regret minimization has proven to be a very powerful tool in both computational learning theory and online algorithms. Regret minimization algorithms can guarantee, for a single decision maker, a near optimal behavior under fairly adversarial assumptions. I will discuss a recent extensions of the classical regret minimization model, which enable to handle many different settings related to job scheduling, and guarantee the near optimal online behavior. 1 Regret Minimization Consider a single decision maker attempting to optimize it performance in face of an uncertain environment. This simple online setting has attracted attention from multiple disciplines, including operations research, game theory, and computer science. In computer science, computational learning theory and online algorithms both focus on this task from different perspectives. I will concentrate only on a certain facet of this general issue of decision making, and consider settings related to regret minimization, where the performance of the online decision
Approximation Algorithms for Offline Riskaverse Combinatorial Optimization
, 2010
"... We consider generic optimization problems that can be formulated as minimizing the cost of a feasible solution w T x over a combinatorial feasible set F ⊂ {0, 1} n. For these problems we describe a framework of riskaverse stochastic problems where the cost vector W has independent random components ..."
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We consider generic optimization problems that can be formulated as minimizing the cost of a feasible solution w T x over a combinatorial feasible set F ⊂ {0, 1} n. For these problems we describe a framework of riskaverse stochastic problems where the cost vector W has independent random components, unknown at the time of solution. A natural and important objective that incorporates risk in this stochastic setting is to look for a feasible solution whose stochastic cost has a small tail or a small convex combination of mean and standard deviation. Our models can be equivalently reformulated as nonconvex programs for which no efficient algorithms are known. In this paper, we make progress on these hard problems. Our results are several efficient generalpurpose approximation schemes. They use as a blackbox (exact or approximate) the solution to the underlying deterministic problem and thus immediately apply to arbitrary combinatorial problems. For example, from an available δapproximation algorithm to the linear problem, we construct a δ(1 + ǫ)approximation algorithm for the stochastic problem, which invokes the linear algorithm only a logarithmic number of times in the problem input (and polynomial in 1 ǫ), for any desired accuracy level ǫ> 0. The algorithms are based on a geometric analysis of the curvature and approximability of the nonlinear level sets of the objective functions. 1
Randomized Sensing in Adversarial Environments
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... How should we manage a sensor network to optimally guard securitycritical infrastructure? How should we coordinate search and rescue helicopters to best locate survivors after a major disaster? In both applications, we would like to control sensing resources in uncertain, adversarial environments. ..."
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How should we manage a sensor network to optimally guard securitycritical infrastructure? How should we coordinate search and rescue helicopters to best locate survivors after a major disaster? In both applications, we would like to control sensing resources in uncertain, adversarial environments. In this paper, we introduce RSENSE, an efficient algorithm which guarantees nearoptimal randomized sensing strategies whenever the detection performance satisfies submodularity, a natural diminishing returns property, for any fixed adversarial scenario. Our approach combines techniques from game theory with submodular optimization. The RSENSE algorithm applies to settings where the goal is to manage a deployed sensor network or to coordinate mobile sensing resources (such as unmanned aerial vehicles). We evaluate our algorithms on two real–world sensing problems.
Online algorithms for submodular minimization with combinatorial constraints
 In Proc. ICML
, 2011
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Playing nonlinear games with linear oracles
 IN FOCS
, 2013
"... Linear optimization is many times algorithmically simpler than nonlinear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have efficient combinatorial algorithms, but whose nonlinear convex counterpart is ha ..."
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Linear optimization is many times algorithmically simpler than nonlinear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have efficient combinatorial algorithms, but whose nonlinear convex counterpart is harder and admit significantly less efficient algorithms. This motivates the computational model of online decision making and optimization using a linear optimization oracle. In this computational model we give the first efficient decision making algorithm with optimal regret guarantees, answering an open question of [1], [2], in case the decision set is a polytope. We also give an extension of the algorithm for the partial information setting, i.e. the “bandit ” model. Our method is based on a novel variant of the conditional gradient method, or FrankWolfe algorithm, that reduces the task of minimizing a smooth convex function over a domain to that of minimizing a linear objective. Whereas previous variants of this method give rise to approximation algorithms, we give such algorithm that converges exponentially faster and thus runs in polynomialtime for a large class of convex optimization problems over polyhedral sets, a result of independent interest.