122 research outputs found
Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round
Many algorithms that are originally designed without explicitly considering
incentive properties are later combined with simple pricing rules and used as
mechanisms. The resulting mechanisms are often natural and simple to
understand. But how good are these algorithms as mechanisms? Truthful reporting
of valuations is typically not a dominant strategy (certainly not with a
pay-your-bid, first-price rule, but it is likely not a good strategy even with
a critical value, or second-price style rule either). Our goal is to show that
a wide class of approximation algorithms yields this way mechanisms with low
Price of Anarchy.
The seminal result of Lucier and Borodin [SODA 2010] shows that combining a
greedy algorithm that is an -approximation algorithm with a
pay-your-bid payment rule yields a mechanism whose Price of Anarchy is
. In this paper we significantly extend the class of algorithms for
which such a result is available by showing that this close connection between
approximation ratio on the one hand and Price of Anarchy on the other also
holds for the design principle of relaxation and rounding provided that the
relaxation is smooth and the rounding is oblivious.
We demonstrate the far-reaching consequences of our result by showing its
implications for sparse packing integer programs, such as multi-unit auctions
and generalized matching, for the maximum traveling salesman problem, for
combinatorial auctions, and for single source unsplittable flow problems. In
all these problems our approach leads to novel simple, near-optimal mechanisms
whose Price of Anarchy either matches or beats the performance guarantees of
known mechanisms.Comment: Extended abstract appeared in Proc. of 16th ACM Conference on
Economics and Computation (EC'15
Fast Convex Decomposition for Truthful Social Welfare Approximation
Approximating the optimal social welfare while preserving truthfulness is a
well studied problem in algorithmic mechanism design. Assuming that the social
welfare of a given mechanism design problem can be optimized by an integer
program whose integrality gap is at most , Lavi and Swamy~\cite{Lavi11}
propose a general approach to designing a randomized -approximation
mechanism which is truthful in expectation. Their method is based on
decomposing an optimal solution for the relaxed linear program into a convex
combination of integer solutions. Unfortunately, Lavi and Swamy's decomposition
technique relies heavily on the ellipsoid method, which is notorious for its
poor practical performance. To overcome this problem, we present an alternative
decomposition technique which yields an approximation
and only requires a quadratic number of calls to an integrality gap verifier
Mechanism Design via Dantzig-Wolfe Decomposition
In random allocation rules, typically first an optimal fractional point is
calculated via solving a linear program. The calculated point represents a
fractional assignment of objects or more generally packages of objects to
agents. In order to implement an expected assignment, the mechanism designer
must decompose the fractional point into integer solutions, each satisfying
underlying constraints. The resulting convex combination can then be viewed as
a probability distribution over feasible assignments out of which a random
assignment can be sampled. This approach has been successfully employed in
combinatorial optimization as well as mechanism design with or without money.
In this paper, we show that both finding the optimal fractional point as well
as its decomposition into integer solutions can be done at once. We propose an
appropriate linear program which provides the desired solution. We show that
the linear program can be solved via Dantzig-Wolfe decomposition. Dantzig-Wolfe
decomposition is a direct implementation of the revised simplex method which is
well known to be highly efficient in practice. We also show how to use the
Benders decomposition as an alternative method to solve the problem. The
proposed method can also find a decomposition into integer solutions when the
fractional point is readily present perhaps as an outcome of other algorithms
rather than linear programming. The resulting convex decomposition in this case
is tight in terms of the number of integer points according to the
Carath{\'e}odory's theorem
Dynamic resource provisioning in cloud computing: A randomized auction approach
Abstract—This work studies resource allocation in a cloud market through the auction of Virtual Machine (VM) instances. It generalizes the existing literature by introducing combinatorial auctions of heterogeneous VMs, and models dynamic VM pro-visioning. Social welfare maximization under dynamic resource provisioning is proven NP-hard, and modeled with a linear inte-ger program. An efficient α-approximation algorithm is designed, with α ∼ 2.72 in typical scenarios. We then employ this algorithm as a building block for designing a randomized combinatorial auction that is computationally efficient, truthful in expectation, and guarantees the same social welfare approximation factor α. A key technique in the design is to utilize a pair of tailored primal and dual LPs for exploiting the underlying packing structure of the social welfare maximization problem, to decompose its fractional solution into a convex combination of integral solutions. Empirical studies driven by Google Cluster traces verify the efficacy of the randomized auction. I
Heuristic methods for the periodic Shipper Lane Selection Problem in transportation auctions
none3siopenTriki, Chefi; Mirmohammadsadeghi, Seyedmehdi; Piya, SujanTriki, Chefi; Mirmohammadsadeghi, Seyedmehdi; Piya, Suja
From Bandits to Experts: On the Value of Side-Observations
We consider an adversarial online learning setting where a decision maker can
choose an action in every stage of the game. In addition to observing the
reward of the chosen action, the decision maker gets side observations on the
reward he would have obtained had he chosen some of the other actions. The
observation structure is encoded as a graph, where node i is linked to node j
if sampling i provides information on the reward of j. This setting naturally
interpolates between the well-known "experts" setting, where the decision maker
can view all rewards, and the multi-armed bandits setting, where the decision
maker can only view the reward of the chosen action. We develop practical
algorithms with provable regret guarantees, which depend on non-trivial
graph-theoretic properties of the information feedback structure. We also
provide partially-matching lower bounds.Comment: Presented at the NIPS 2011 conferenc
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