89,726 research outputs found

    Budget Feasible Mechanisms for Experimental Design

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    In the classical experimental design setting, an experimenter E has access to a population of nn potential experiment subjects i{1,...,n}i\in \{1,...,n\}, each associated with a vector of features xiRdx_i\in R^d. Conducting an experiment with subject ii reveals an unknown value yiRy_i\in R to E. E typically assumes some hypothetical relationship between xix_i's and yiy_i's, e.g., yiβxiy_i \approx \beta x_i, and estimates β\beta from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget BB. Each subject ii declares an associated cost ci>0c_i >0 to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set SS of subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) under the constraint iSciB\sum_{i\in S}c_i\leq B; our objective function corresponds to the information gain in parameter β\beta that is learned through linear regression methods, and is related to the so-called DD-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small δ>0\delta > 0 and ϵ>0\epsilon > 0, we can construct a (12.98, ϵ\epsilon)-approximate mechanism that is δ\delta-truthful and runs in polynomial time in both nn and loglogBϵδ\log\log\frac{B}{\epsilon\delta}. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression

    Coverage, Matching, and Beyond: New Results on Budgeted Mechanism Design

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    We study a type of reverse (procurement) auction problems in the presence of budget constraints. The general algorithmic problem is to purchase a set of resources, which come at a cost, so as not to exceed a given budget and at the same time maximize a given valuation function. This framework captures the budgeted version of several well known optimization problems, and when the resources are owned by strategic agents the goal is to design truthful and budget feasible mechanisms, i.e. elicit the true cost of the resources and ensure the payments of the mechanism do not exceed the budget. Budget feasibility introduces more challenges in mechanism design, and we study instantiations of this problem for certain classes of submodular and XOS valuation functions. We first obtain mechanisms with an improved approximation ratio for weighted coverage valuations, a special class of submodular functions that has already attracted attention in previous works. We then provide a general scheme for designing randomized and deterministic polynomial time mechanisms for a class of XOS problems. This class contains problems whose feasible set forms an independence system (a more general structure than matroids), and some representative problems include, among others, finding maximum weighted matchings, maximum weighted matroid members, and maximum weighted 3D-matchings. For most of these problems, only randomized mechanisms with very high approximation ratios were known prior to our results

    How to Allocate R&D (and Other) Subsidies: An Experimentally Tested Policy Recommendation

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    This paper evaluates how R&D subsidies to the business sector are typically awarded. We identify two sources of ine_ciency: the selection based on a ranking of individual projects, rather than complete allocations, and the failure to induce competition among applicants in order to extract and use information about the necessary funding. In order to correct these ine_- ciencies we propose mechanisms that include some form of an auction in which applicants bid for subsidies. Our proposals are tested in a simulation and in controlled lab experiments. The results suggest that adopting our proposals may considerably improve the allocation

    Information Gathering with Peers: Submodular Optimization with Peer-Prediction Constraints

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    We study a problem of optimal information gathering from multiple data providers that need to be incentivized to provide accurate information. This problem arises in many real world applications that rely on crowdsourced data sets, but where the process of obtaining data is costly. A notable example of such a scenario is crowd sensing. To this end, we formulate the problem of optimal information gathering as maximization of a submodular function under a budget constraint, where the budget represents the total expected payment to data providers. Contrary to the existing approaches, we base our payments on incentives for accuracy and truthfulness, in particular, {\em peer-prediction} methods that score each of the selected data providers against its best peer, while ensuring that the minimum expected payment is above a given threshold. We first show that the problem at hand is hard to approximate within a constant factor that is not dependent on the properties of the payment function. However, for given topological and analytical properties of the instance, we construct two greedy algorithms, respectively called PPCGreedy and PPCGreedyIter, and establish theoretical bounds on their performance w.r.t. the optimal solution. Finally, we evaluate our methods using a realistic crowd sensing testbed.Comment: Longer version of AAAI'18 pape

    Budget-Feasible Mechanism Design for Non-Monotone Submodular Objectives: Offline and Online

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    The framework of budget-feasible mechanism design studies procurement auctions where the auctioneer (buyer) aims to maximize his valuation function subject to a hard budget constraint. We study the problem of designing truthful mechanisms that have good approximation guarantees and never pay the participating agents (sellers) more than the budget. We focus on the case of general (non-monotone) submodular valuation functions and derive the first truthful, budget-feasible and O(1)O(1)-approximate mechanisms that run in polynomial time in the value query model, for both offline and online auctions. Prior to our work, the only O(1)O(1)-approximation mechanism known for non-monotone submodular objectives required an exponential number of value queries. At the heart of our approach lies a novel greedy algorithm for non-monotone submodular maximization under a knapsack constraint. Our algorithm builds two candidate solutions simultaneously (to achieve a good approximation), yet ensures that agents cannot jump from one solution to the other (to implicitly enforce truthfulness). Ours is the first mechanism for the problem where---crucially---the agents are not ordered with respect to their marginal value per cost. This allows us to appropriately adapt these ideas to the online setting as well. To further illustrate the applicability of our approach, we also consider the case where additional feasibility constraints are present. We obtain O(p)O(p)-approximation mechanisms for both monotone and non-monotone submodular objectives, when the feasible solutions are independent sets of a pp-system. With the exception of additive valuation functions, no mechanisms were known for this setting prior to our work. Finally, we provide lower bounds suggesting that, when one cares about non-trivial approximation guarantees in polynomial time, our results are asymptotically best possible.Comment: Accepted to EC 201

    On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives

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    We study a class of procurement auctions with a budget constraint, where an auctioneer is interested in buying resources or services from a set of agents. Ideally, the auctioneer would like to select a subset of the resources so as to maximize his valuation function, without exceeding a given budget. As the resources are owned by strategic agents however, our overall goal is to design mechanisms that are truthful, budget-feasible, and obtain a good approximation to the optimal value. Budget-feasibility creates additional challenges, making several approaches inapplicable in this setting. Previous results on budget-feasible mechanisms have considered mostly monotone valuation functions. In this work, we mainly focus on symmetric submodular valuations, a prominent class of non-monotone submodular functions that includes cut functions. We begin first with a purely algorithmic result, obtaining a 2ee1\frac{2e}{e-1}-approximation for maximizing symmetric submodular functions under a budget constraint. We view this as a standalone result of independent interest, as it is the best known factor achieved by a deterministic algorithm. We then proceed to propose truthful, budget feasible mechanisms (both deterministic and randomized), paying particular attention on the Budgeted Max Cut problem. Our results significantly improve the known approximation ratios for these objectives, while establishing polynomial running time for cases where only exponential mechanisms were known. At the heart of our approach lies an appropriate combination of local search algorithms with results for monotone submodular valuations, applied to the derived local optima.Comment: A conference version appears in WINE 201

    How to Allocate R&D (and Other) Subsidies: An Experimentally Tested Policy Recommendation

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    This paper evaluates how R&D subsidies to the business sector are typically awarded. We identify two sources of ine_ciency: the selection based on a ranking of individual projects, rather than complete allocations, and the failure to induce competition among applicants in order to extract and use information about the necessary funding. In order to correct these ine_- ciencies we propose mechanisms that include some form of an auction in which applicants bid for subsidies. Our proposals are tested in a simulation and in controlled lab experiments. The results suggest that adopting our proposals may considerably improve the allocation.Research; Subsidies; Experimental Economics
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