128 research outputs found
Truth and Regret in Online Scheduling
We consider a scheduling problem where a cloud service provider has multiple
units of a resource available over time. Selfish clients submit jobs, each with
an arrival time, deadline, length, and value. The service provider's goal is to
implement a truthful online mechanism for scheduling jobs so as to maximize the
social welfare of the schedule. Recent work shows that under a stochastic
assumption on job arrivals, there is a single-parameter family of mechanisms
that achieves near-optimal social welfare. We show that given any such family
of near-optimal online mechanisms, there exists an online mechanism that in the
worst case performs nearly as well as the best of the given mechanisms. Our
mechanism is truthful whenever the mechanisms in the given family are truthful
and prompt, and achieves optimal (within constant factors) regret.
We model the problem of competing against a family of online scheduling
mechanisms as one of learning from expert advice. A primary challenge is that
any scheduling decisions we make affect not only the payoff at the current
step, but also the resource availability and payoffs in future steps.
Furthermore, switching from one algorithm (a.k.a. expert) to another in an
online fashion is challenging both because it requires synchronization with the
state of the latter algorithm as well as because it affects the incentive
structure of the algorithms. We further show how to adapt our algorithm to a
non-clairvoyant setting where job lengths are unknown until jobs are run to
completion. Once again, in this setting, we obtain truthfulness along with
asymptotically optimal regret (within poly-logarithmic factors)
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On Revenue-Optimal Dynamic Auctions for Bidders with Interdependent Values
In a dynamic market, being able to update one’s value based on information available to other bidders currently in the market can be critical to having profitable transactions. This is nicely captured by the model of interdependent values (IDV): a bidder’s value can explicitly depend on the private information of other bidders. In this paper we present preliminary results about the revenue properties of dynamic auctions for IDV bidders. We adopt a computational approach to design single-item revenue-optimal dynamic auctions with known arrivals and departures but (private) signals that arrive online. In leveraging a characterization of truthful auctions, we present a mixed-integer programming formulation of the design problem. Although a discretization is imposed on bidder signals the solution is a mechanism applicable to continuous signals. The formulation size grows exponentially in the dependence of bidders’ values on other bidders’ signals. We highlight general properties of revenue-optimal dynamic auctions in a simple parametrized example and study the sensitivity of prices and revenue to model parameters.Engineering and Applied Science
On the Interplay between Social Welfare and Tractability of Equilibria
Computational tractability and social welfare (aka. efficiency) of equilibria
are two fundamental but in general orthogonal considerations in algorithmic
game theory. Nevertheless, we show that when (approximate) full efficiency can
be guaranteed via a smoothness argument \`a la Roughgarden, Nash equilibria are
approachable under a family of no-regret learning algorithms, thereby enabling
fast and decentralized computation. We leverage this connection to obtain new
convergence results in large games -- wherein the number of players
-- under the well-documented property of full efficiency via smoothness in the
limit. Surprisingly, our framework unifies equilibrium computation in disparate
classes of problems including games with vanishing strategic sensitivity and
two-player zero-sum games, illuminating en route an immediate but overlooked
equivalence between smoothness and a well-studied condition in the optimization
literature known as the Minty property. Finally, we establish that a family of
no-regret dynamics attains a welfare bound that improves over the smoothness
framework while at the same time guaranteeing convergence to the set of coarse
correlated equilibria. We show this by employing the clairvoyant mirror descent
algortihm recently introduced by Piliouras et al.Comment: To appear at NeurIPS 202
08071 Abstracts Collection -- Scheduling
From 10.02. to 15.02., the Dagstuhl Seminar 08071 ``Scheduling\u27\u27 was held
in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Incentive-aware Contextual Pricing with Non-parametric Market Noise
We consider a dynamic pricing problem for repeated contextual second-price
auctions with strategic buyers whose goals are to maximize their long-term time
discounted utility. The seller has very limited information about buyers'
overall demand curves, which depends on -dimensional context vectors
characterizing auctioned items, and a non-parametric market noise distribution
that captures buyers' idiosyncratic tastes. The noise distribution and the
relationship between the context vectors and buyers' demand curves are both
unknown to the seller. We focus on designing the seller's learning policy to
set contextual reserve prices where the seller's goal is to minimize his regret
for revenue. We first propose a pricing policy when buyers are truthful and
show that it achieves a -period regret bound of
against a clairvoyant policy that has full
information of the buyers' demand. Next, under the setting where buyers bid
strategically to maximize their long-term discounted utility, we develop a
variant of our first policy that is robust to strategic (corrupted) bids. This
policy incorporates randomized "isolation" periods, during which a buyer is
randomly chosen to solely participate in the auction. We show that this design
allows the seller to control the number of periods in which buyers
significantly corrupt their bids. Because of this nice property, our robust
policy enjoys a -period regret of , matching
that under the truthful setting up to a constant factor that depends on the
utility discount factor
Online Pandora's Boxes and Bandits
We consider online variations of the Pandora's box problem (Weitzman. 1979),
a standard model for understanding issues related to the cost of acquiring
information for decision-making. Our problem generalizes both the classic
Pandora's box problem and the prophet inequality framework. Boxes are presented
online, each with a random value and cost drew jointly from some known
distribution. Pandora chooses online whether to open each box given its cost,
and then chooses irrevocably whether to keep the revealed prize or pass on it.
We aim for approximation algorithms against adversaries that can choose the
largest prize over any opened box, and use optimal offline policies to decide
which boxes to open (without knowledge of the value inside). We consider
variations where Pandora can collect multiple prizes subject to feasibility
constraints, such as cardinality, matroid, or knapsack constraints. We also
consider variations related to classic multi-armed bandit problems from
reinforcement learning. Our results use a reduction-based framework where we
separate the issues of the cost of acquiring information from the online
decision process of which prizes to keep. Our work shows that in many
scenarios, Pandora can achieve a good approximation to the best possible
performance
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