103 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
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Bayesian Auction Design and Approximation
We study two classes of problems within Algorithmic Economics: revenue guarantees of simple mechanisms, and social welfare guarantees of auctions. We develop new structural and algorithmic tools for addressing these problems, and obtain the following results:
In the -unit model, four canonical mechanisms can be classified as: (i) the discriminating group, including Myerson Auction and Sequential Posted-Pricing, and (ii) the anonymous group, including Anonymous Reserve and Anonymous Pricing. We prove that any two mechanisms from the same group have an asymptotically tight revenue gap of 1 + θ(1 /â), while any two mechanisms from the different groups have an asymptotically tight revenue gap of θ(log ).
In the single-item model, we prove a nearly-tight sample complexity of Anonymous Reserve for every value distribution family investigated in the literature: [0, 1]-bounded, [1, ]-bounded, regular, and monotone hazard rate (MHR).
Remarkably, the setting-specific sample complexity poly(âťÂš) depends on the precision â (0, 1), but not on the number of bidders ⼠1. Further, in the two bounded-support settings, our algorithm allows correlated value distributions. These are in sharp contrast to the previous (nearly-tight) sample complexity results on Myerson Auction.
In the single-item model, we prove that the tight Price of Anarchy/Stability for First Price Auctions are both PoA = PoS = 1 - 1/² â 0.8647
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
A Primal-Dual Analysis of Monotone Submodular Maximization
In this paper we design a new primal-dual algorithm for the classic discrete
optimization problem of maximizing a monotone submodular function subject to a
cardinality constraint achieving the optimal approximation of . This
problem and its special case, the maximum -coverage problem, have a wide
range of applications in various fields including operations research, machine
learning, and economics. While greedy algorithms have been known to achieve
this approximation factor, our algorithms also provide a dual certificate which
upper bounds the optimum value of any instance. This certificate may be used in
practice to certify much stronger guarantees than the worst-case
approximation factor
Relational learning for set value functions
Relational learning is learning in a context where we have a set of items with relationships. For example, in a recommender system or advertising platform, items are grouped into lists to attract user attention, and some items may be more popular than others. We are often interested in learning individual abilities, approximating group performances and making best set selection. However, it could be challenging as we have limited feedback and various uncertainties. We might only observe noisy aggregate feedback at the set level (set level randomness), and each item could be a random variable following some distributions (item level randomness). To tackle the problem, we model the group performance using a set value function, defined as a function of item values within the group of interest. We first study the beta model for hypergraphs. The model treats relational data as hypergraphs where nodes represent items and hyper-edges group items into sets. The goal is to estimate individual beta values from the group outcomes. We study the inference problem under different settings using maximum likelihood estimation (MLE). We move on to consider more general set value functions and the second source of randomness at the item level. The goal is to find good item representations (sketches) for approximation of stochastic valuation functions, defined as the expectation of set value functions of independent random variables. We present an approximation everywhere guarantee for a wide range of stochastic valuation functions. Finally, we study an online variant where an agent can draw samples sequentially. At each time step, the agent chooses a group of items subject to constraints and receives some form of feedbacks. The goal is to select a set of items with maximum performances according to some stochastic valuation functions. We consider the regret minimization setting and address the problem under value-index feedback
Learning and Robustness With Applications To Mechanism Design
The design of economic mechanisms, especially auctions, is an increasingly important part of the modern economy. A particularly important property for a mechanism is strategyproofness -- the mechanism must be robust to strategic manipulations so that the participants in the mechanism have no incentive to lie. Yet in the important case when the mechanism designer's goal is to maximize their own revenue, the design of optimal strategyproof mechanisms has proved immensely difficult, with very little progress after decades of research.
Recently, to escape this impasse, a number of works have parameterized auction mechanisms as deep neural networks, and used gradient descent to successfully learn approximately optimal and approximately strategyproof mechanisms. We present several improvements on these techniques.
When an auction mechanism is represented as a neural network mapping bids from outcomes, strategyproofness can be thought of as a type of adversarial robustness. Making this connection explicit, we design a modified architecture for learning auctions which is amenable to integer-programming-based certification techniques from the adversarial robustness literature. Existing baselines are empirically strategyproof, but with no way to be certain how strong that guarantee really is. By contrast, we are able to provide perfectly tight bounds on the degree to which strategyproofness is violated at any given point.
Existing neural networks for auctions learn to maximize revenue subject to strategyproofness. Yet in many auctions, fairness is also an important concern -- in particular, fairness with respect to the items in the auction, which may represent, for instance, ad impressions for different protected demographic groups. With our new architecture, ProportionNet, we impose fairness constraints in addition to the strategyproofness constraints, and find approximately fair, approximately optimal mechanisms which outperform baselines. With PreferenceNet, we extend this approach to notions of fairness that are learned from possibly vague human preferences.
Existing network architectures can represent additive and unit-demand auctions, but are unable to imposing more complex exactly-k constraints on the allocations made to the bidders. By using the Sinkhorn algorithm to add differentiable matching constraints, we produce a network which can represent valid allocations in such settings.
Finally, we present a new auction architecture which is a differentiable version of affine maximizer auctions, modified to offer lotteries in order to potentially increase revenue. This architecture is always perfectly strategyproof (avoiding the Lagrangian-based constrained optimization of RegretNet) -- to achieve this goal, however, we need to accept that we cannot in general represent the optimal auction
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Forecasting and Risk Management Techniques for Electricity Markets
This book focuses on the recent development of forecasting and risk management techniques for electricity markets. In addition, we discuss research on new trading platforms and environments using blockchain-based peer-to-peer (P2P) markets and computer agents. The book consists of two parts. The first part is entitled âForecasting and Risk Management Techniquesâ and contains five chapters related to weather and electricity derivatives, and load and price forecasting for supporting electricity trading. The second part is entitled âPeer-to-Peer (P2P) Electricity Trading System and Strategyâ and contains the following five chapters related to the feasibility and enhancement of P2P energy trading from various aspects
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