From convex optimization to randomized mechanisms

Dughmi, Shaddin; Roughgarden, Tim; Yan, Qiqi

doi:10.1145/1993636.1993657

Cited by 59 publications

(105 citation statements)

References 25 publications

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“…The state-of-the-art without concern for incentives is a 1/2-approximation for any number of subadditive bidders [29], and numerous improvements for special cases, such as submodular bidders [23,29,30]. With concern for incentives, the state-of-the-art (for worst-case approximation ratios and dominant strategy truthfulness) is an 1/O( √ log m)-approximation for XOS bidders, again with improvements for further special cases [26]. The problem has also been studied in Bayesian settings, where a generic black-box reduction is known if the designer only desires Bayesian truthfulness 15 [36,35,5].…”

Section: A Background On Related Workmentioning

confidence: 99%

On Simultaneous Two-player Combinatorial Auctions

Braverman

Mao

Weinberg

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider the following communication problem: Alice and Bob each have some valuation functions v 1 (·) and v 2 (·) over subsets of m items, and their goal is to partition the items into S,S in a way that maximizes the welfare, v 1 (S)+v 2 (S). We study both the allocation problem, which asks for a welfare-maximizing partition and the decision problem, which asks whether or not there exists a partition guaranteeing certain welfare, for binary XOS valuations. For interactive protocols with poly(m) communication, a tight 3/4-approximation is known for both [29,23].For interactive protocols, the allocation problem is provably harder than the decision problem: any solution to the allocation problem implies a solution to the decision problem with one additional round and log m additional bits of communication via a trivial reduction. Surprisingly, the allocation problem is provably easier for simultaneous protocols. Specifically, we show:• There exists a simultaneous, randomized protocol with polynomial communication that selects a partition whose expected welfare is at least 3/4 of the optimum. This matches the guarantee of the best interactive, randomized protocol with polynomial communication.• For all ε > 0, any simultaneous, randomized protocol that decides whether the welfare of the optimal partition is ≥ 1 or ≤ 3/4 − 1/108 + ε correctly with probability > 1/2 + 1/poly(m) requires exponential communication. (≤ 3/4 − 1/108) protocols with polynomial communication. In other words, this trivial reduction from decision to allocation problems provably requires the extra round of communication. We further discuss the implications of our results for the design of truthful combinatorial auctions in general, and extensions to general XOS valuations. In particular, our protocol for the allocation problem implies a new style of truthful mechanisms. IntroductionIntuitively, search problems (find the optimal solution) are considered "strictly harder" than decision problems (does a solution with quality ≥ Q exist?) for the following (formal) reason: once you find the optimal solution, you can simply evaluate it and check whether its quality is ≥ Q or not. The same intuition carries over to approximation as well: once you find a solution whose quality is within a factor α of optimal, you can distinguish between cases where solutions with quality ≥ Q exist and those where all solutions have quality ≤ αQ. The easy conclusion one then draws is that the communication (resp. runtime) required for an α-approximation to any decision problem is upper bounded by the communication (resp. runtime) required for an α-approximation to the corresponding search problem plus the communication (resp. runtime) required to evaluate the quality of a proposed solution.Note though that for communication problems, in addition to the negligible increase in communication (due to evaluating the quality of the proposed solution), this simple reduction might also require (at least) an extra round of communication (because the parties can evalua...

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Section: A Background On Related Workmentioning

confidence: 99%

On Simultaneous Two-player Combinatorial Auctions

Braverman

Mao

Weinberg

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Since then, combinatorial auctions and combinatorial public projects have emerged as the paradigmatic "challenge problems" of the field, with much work in recent years establishing upper and lower bounds on truthful polynomial-time mechanisms for these problems (e.g. [36,16,18,17,15,11,19,47,7,8,12,24,21,25,20]). The most general approach known for designing (randomized) truthful mechanisms is via maximal-in-distributional range (MIDR) algorithms [13,22].…”

Section: The Challenge Of Algorithmic Mechanism Designmentioning

confidence: 99%

“…However, payment scheme p vcg may not be implementable efficiently, due to the difficulty in exactly evaluating the expectations in expression (24). Nevertheless, it is an easy observation that any payment scheme p with E[p i (v)] = p vcg i (v) for each i and v yields the same guarantees in expectation.…”

Section: B2 Computing Paymentsmentioning

confidence: 99%

Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

Dughmi

Roughgarden

Yan

2016

J. ACM

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We design the first truthful-in-expectation, constant-factor approximation mechanisms for N P -hard cases of the welfare maximization problem in combinatorial auctions with non-identical items and in combinatorial public projects. Our results apply to bidders with valuations that are nonnegative linear combinations of gross substitutes valuations, a class that encompasses many of the most well-studied subclasses of submodular functions, including coverage functions and weighted matroid rank functions. Our mechanisms have expected polynomial running time and achieve an approximation factor of 1 − 1/e. This approximation factor is the best possible for both problems, even for known and explicitly given coverage valuations, assuming P = N P . Recent impossibility results suggest that our results cannot be extended to a significantly larger valuation class.Both of our mechanisms are instantiations of a new framework for designing approximation mechanisms based on randomized rounding algorithms. The high-level idea of this framework is to optimize directly over the (random) output of the rounding algorithm, rather than the usual (and rarely truthful) approach of optimizing over the input to the rounding algorithm. This framework yields truthful-in-expectation mechanisms, and these mechanisms can be implemented efficiently when the corresponding objective function is concave. For bidders with valuations in the cone generated by gross substitutes valuations, we give novel randomized rounding algorithms that lead to both a concave objective function and a (1 − 1/e)-approximation of the optimal welfare. * Preliminary versions of this work appeared in

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“…Lavi and Swamy [15] consider mechanisms for multi-parameter packing problems and show how to construct a (randomized) TIE β-approximation mechanism from any β-approximation that verifies an integrality gap. Dughmi, Roughgarden and Yan [9] extend this approach and obtain TIE mechanisms for a broad class of submodular combinatorial auctions. Dughmi and Roughgarden [8] give a construction that converts any FPTAS algorithm for a social welfare problem into a TIE mechanism.…”

Section: Related Workmentioning

confidence: 99%

On the limits of black-box reductions in mechanism design

Chawla

Immorlica

Lucier

2012

Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing

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We consider the problem of converting an arbitrary approximation algorithm for a single-parameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are black-box, meaning that they require only oracle access to the given algorithm and in particular do not require explicit knowledge of the problem constraints. Such a reduction is known to be possible, for example, for the social welfare objective when the goal is to achieve Bayesian truthfulness and preserve social welfare in expectation. We show that a black-box reduction for the social welfare objective is not possible if the resulting mechanism is required to be truthful in expectation and to preserve the worst-case approximation ratio of the algorithm to within a subpolynomial factor. Further, we prove that for other objectives such as makespan, no black-box reduction is possible even if we only require Bayesian truthfulness and an average-case performance guarantee.

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From convex optimization to randomized mechanisms

Cited by 59 publications

References 25 publications

On Simultaneous Two-player Combinatorial Auctions

On Simultaneous Two-player Combinatorial Auctions

Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

On the limits of black-box reductions in mechanism design

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