454,189 research outputs found
The Complexity of Optimal Mechanism Design
Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders [18]. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a revenue-optimal auction in multi-item settings cannot be found and implemented computationally efficiently, unless zpp ⊇ P[superscript #P]. This is true even for a single additive bidder whose values for the items are independently distributed on two rational numbers with rational probabilities. Our result is very general: we show that it is hard to compute any encoding of an optimal auction of any format (direct or indirect, truthful or non-truthful) that can be implemented in expected polynomial time. In particular, under well-believed complexity-theoretic assumptions, revenue-optimization in very simple multi-item settings can only be tractably approximated.
We note that our hardness result applies to randomized mechanisms in a very simple setting, and is not an artifact of introducing combinatorial structure to the problem by allowing correlation among item values, introducing combinatorial valuations, or requiring the mechanism to be deterministic (whose structure is readily combinatorial). Our proof is enabled by a flow-interpretation of the solutions of an exponential-size linear program for revenue maximization with an additional supermodularity constraint.Alfred P. Sloan Foundation (Fellowship)Microsoft Research (Faculty Fellowship)National Science Foundation (U.S.) (CAREER Award CCF-0953960)National Science Foundation (U.S.) (Award CCF-1101491)Hertz Foundation (Daniel Stroock Fellowship
The complexity of optimal mechanism design
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 63-64).Myerson's seminal work provides a computationally efficient revenue-optimal auction for selling one item to multiple bidders. Generalizing this work to selling multiple items at once has been a central question in economics and algorithmic game theory, but its complexity has remained poorly understood. We answer this question by showing that a revenue-optimal auction in multi-item settings cannot be found and implemented computationally efficiently, unless ZPP = P # p. This is true even for a single additive bidder whose values for the items are independently distributed on two rational numbers with rational probabilities. Our result is very general: we show that it is hard to compute any encoding of an optimal auction of any format (direct or indirect, truthful or non-truthful) that can be implemented in expected polynomial time. In particular, under well-believed complexity-theoretic assumptions, revenue-optimization in very simple multi-item settings can only be tractably approximated. We note that our hardness result applies to randomized mechanisms in a very simple setting, and is not an artifact of introducing combinatorial structure to the problem by allowing correlation among item values, introducing combinatorial valuations, or requiring the mechanism to be deterministic (whose structure is readily combinatorial). Our proof is enabled by a flow interpretation of the solutions of an exponential-size linear program for revenue maximization with an additional supermodularity constraint.by Christos Tzamos.S.M
Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned
Optimal mechanism design enjoys a beautiful and well-developed theory, and
also a number of killer applications. Rules of thumb produced by the field
influence everything from how governments sell wireless spectrum licenses to
how the major search engines auction off online advertising. There are,
however, some basic problems for which the traditional optimal mechanism design
approach is ill-suited --- either because it makes overly strong assumptions,
or because it advocates overly complex designs. The thesis of this paper is
that approximately optimal mechanisms allow us to reason about fundamental
questions that seem out of reach of the traditional theory.
This survey has three main parts. The first part describes the approximately
optimal mechanism design paradigm --- how it works, and what we aim to learn by
applying it. The second and third parts of the survey cover two case studies,
where we instantiate the general design paradigm to investigate two basic
questions. In the first example, we consider revenue maximization in a
single-item auction with heterogeneous bidders. Our goal is to understand if
complexity --- in the sense of detailed distributional knowledge --- is an
essential feature of good auctions for this problem, or alternatively if there
are simpler auctions that are near-optimal. The second example considers
welfare maximization with multiple items. Our goal here is similar in spirit:
when is complexity --- in the form of high-dimensional bid spaces --- an
essential feature of every auction that guarantees reasonable welfare? Are
there interesting cases where low-dimensional bid spaces suffice?Comment: Based on a talk given by the author at the 15th ACM Conference on
Economics and Computation (EC), June 201
Learning Complexity-Aware Cascades for Deep Pedestrian Detection
The design of complexity-aware cascaded detectors, combining features of very
different complexities, is considered. A new cascade design procedure is
introduced, by formulating cascade learning as the Lagrangian optimization of a
risk that accounts for both accuracy and complexity. A boosting algorithm,
denoted as complexity aware cascade training (CompACT), is then derived to
solve this optimization. CompACT cascades are shown to seek an optimal
trade-off between accuracy and complexity by pushing features of higher
complexity to the later cascade stages, where only a few difficult candidate
patches remain to be classified. This enables the use of features of vastly
different complexities in a single detector. In result, the feature pool can be
expanded to features previously impractical for cascade design, such as the
responses of a deep convolutional neural network (CNN). This is demonstrated
through the design of a pedestrian detector with a pool of features whose
complexities span orders of magnitude. The resulting cascade generalizes the
combination of a CNN with an object proposal mechanism: rather than a
pre-processing stage, CompACT cascades seamlessly integrate CNNs in their
stages. This enables state of the art performance on the Caltech and KITTI
datasets, at fairly fast speeds
A General Theory of Sample Complexity for Multi-Item Profit Maximization
The design of profit-maximizing multi-item mechanisms is a notoriously
challenging problem with tremendous real-world impact. The mechanism designer's
goal is to field a mechanism with high expected profit on the distribution over
buyers' values. Unfortunately, if the set of mechanisms he optimizes over is
complex, a mechanism may have high empirical profit over a small set of samples
but low expected profit. This raises the question, how many samples are
sufficient to ensure that the empirically optimal mechanism is nearly optimal
in expectation? We uncover structure shared by a myriad of pricing, auction,
and lottery mechanisms that allows us to prove strong sample complexity bounds:
for any set of buyers' values, profit is a piecewise linear function of the
mechanism's parameters. We prove new bounds for mechanism classes not yet
studied in the sample-based mechanism design literature and match or improve
over the best known guarantees for many classes. The profit functions we study
are significantly different from well-understood functions in machine learning,
so our analysis requires a sharp understanding of the interplay between
mechanism parameters and buyer values. We strengthen our main results with
data-dependent bounds when the distribution over buyers' values is
"well-behaved." Finally, we investigate a fundamental tradeoff in sample-based
mechanism design: complex mechanisms often have higher profit than simple
mechanisms, but more samples are required to ensure that empirical and expected
profit are close. We provide techniques for optimizing this tradeoff
Public projects, Boolean functions and the borders of Border's theorem
Border's theorem gives an intuitive linear characterization of the feasible
interim allocation rules of a Bayesian single-item environment, and it has
several applications in economic and algorithmic mechanism design. All known
generalizations of Border's theorem either restrict attention to relatively
simple settings, or resort to approximation. This paper identifies a
complexity-theoretic barrier that indicates, assuming standard complexity class
separations, that Border's theorem cannot be extended significantly beyond the
state-of-the-art. We also identify a surprisingly tight connection between
Myerson's optimal auction theory, when applied to public project settings, and
some fundamental results in the analysis of Boolean functions.Comment: Accepted to ACM EC 201
Calendar mechanisms
I study the dynamic mechanism design problem of a monopolist selling a fixed number of service slots to randomly arriving, short-lived buyers with heterogeneous values. The fully optimal mechanism is a non-standard auction in which bidders' payoffs are non-monotone in their opponents' bids. Because its complexity may make the fully optimal mechanism too costly to implement, I also study the optimal mechanisms in restricted classes. The most restrictive are pure calendar mechanisms, which allocate service dates instead of contingent contracts. The optimal pure calendar mechanism is characterized by the opportunity costs of service slots and is implementable with a simple mechanism
On the Non-Contractual Nature of Donor-Recipient Interaction in Development Assistance
This paper analyses three issues in strategic donor-recipient interaction motivated by the complexity of the rationale underlying aid. The first is when we have several principals with conflicting objectives. Any one principal cannot offer high powered incentives to the agent to carry out their designated task. The second is to do with the fact that effort associated with ensuring aid effectiveness may concern both principal and agent; the optimal solution to which requires difficult to design cooperative behaviour. Consequently, the contractual type principal-agent relationship between donors and recipients is inappropriate. We need to consider models that signal recipient quality or commitment to reform. A simple model of signalling with commitment problems is presented, along with extensions to multiple types of agents and time periods, as well as possible solutions involving mechanism design.aid, conditionality, contracting, signalling quality, mechanism design
- …