864 research outputs found
Budget-Feasible Mechanism Design for Non-Monotone Submodular Objectives: Offline and Online
The framework of budget-feasible mechanism design studies procurement
auctions where the auctioneer (buyer) aims to maximize his valuation function
subject to a hard budget constraint. We study the problem of designing truthful
mechanisms that have good approximation guarantees and never pay the
participating agents (sellers) more than the budget. We focus on the case of
general (non-monotone) submodular valuation functions and derive the first
truthful, budget-feasible and -approximate mechanisms that run in
polynomial time in the value query model, for both offline and online auctions.
Prior to our work, the only -approximation mechanism known for
non-monotone submodular objectives required an exponential number of value
queries.
At the heart of our approach lies a novel greedy algorithm for non-monotone
submodular maximization under a knapsack constraint. Our algorithm builds two
candidate solutions simultaneously (to achieve a good approximation), yet
ensures that agents cannot jump from one solution to the other (to implicitly
enforce truthfulness). Ours is the first mechanism for the problem
where---crucially---the agents are not ordered with respect to their marginal
value per cost. This allows us to appropriately adapt these ideas to the online
setting as well.
To further illustrate the applicability of our approach, we also consider the
case where additional feasibility constraints are present. We obtain
-approximation mechanisms for both monotone and non-monotone submodular
objectives, when the feasible solutions are independent sets of a -system.
With the exception of additive valuation functions, no mechanisms were known
for this setting prior to our work. Finally, we provide lower bounds suggesting
that, when one cares about non-trivial approximation guarantees in polynomial
time, our results are asymptotically best possible.Comment: Accepted to EC 201
On the Tree Conjecture for the Network Creation Game
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al.[PODC\u2703] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of alpha per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all alpha and that for alpha >= n all equilibrium networks are trees.
We introduce a novel technique for analyzing stable networks for high edge-price alpha and employ it to improve on the best known bounds for both conjectures. In particular we show that for alpha > 4n-13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of alpha. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees
Envy, Regret, and Social Welfare Loss
Incentive compatibility (IC) is a desirable property for any auction mechanism, including those used in online advertising. However, in real world applications practical constraints and complex environments often result in mechanisms that lack incentive compatibility. Recently, several papers investigated the problem of deploying black-box statistical tests to determine if an auction mechanism is incentive compatible by using the notion of IC-Regret that measures the regret of a truthful bidder. Unfortunately, most of those methods are computationally intensive, since they require the execution of many counterfactual experiments. In this work, we show that similar results can be obtained using the notion of IC-Envy. The advantage of IC-Envy is its efficiency: it can be computed using only the auction's outcome. In particular, we focus on position auctions. For position auctions, we show that for a large class of pricing schemes (which includes e.g. VCG and GSP), IC-Envy ≥ IC-Regret (and IC-Envy = IC-Regret under mild supplementary conditions). Our theoretical results are completed showing that, in the position auction environment, IC-Envy can be used to bound the loss in social welfare due to the advertiser untruthful behavior. Finally, we show experimentally that IC-Envy can be used as a feature to predict IC-Regret in settings not covered by the theoretical results. In particular, using IC-Envy yields better results than training models using only price and value features
Budget-feasible mechanism design for non-monotone submodular objectives: Offline and online
The framework of budget-feasible mechanism design studies procurement auctions where the auctioneer (buyer) aims to maximize his valuation function subject to a hard budget constraint. We study the problem of designing truthful mechanisms that have good approximation guarantees and never pay the participating agents (sellers) more than the budget. We focus on the case of general (non-monotone) submodular valuation functions and derive the first truthful, budget-feasible and O(1)-approximation mechanisms that run in polynomial time in the value query model, for both offline and online auctions. Since the introduction of the problem by Singer [40], obtaining efficient mechanisms for objectives that go beyond the class of monotone submodular functions has been elusive. Prior to our work, the only O(1)-approximation mechanism known for non-monotone submodular objectives required an exponential number of value queries. At the heart of our approach lies a novel greedy algorithm for non-monotone submodular maximization under a knapsack constraint. Our algorithm builds two candidate solutions simultaneously (to achieve a good approximation), yet ensures that agents cannot jump from one solution to the other (to implicitly enforce truthfulness). Ours is the first mechanism for the problem where-crucially-the agents are not ordered according to their marginal value per cost. This allows us to appropriately adapt these ideas to the online setting as well. To further illustrate the applicability of our approach, we also consider the case where additional feasibility constraints are present, e.g., at most k agents can be selected. We obtain O(p)-approximation mechanisms for both monotone and non-monotone submodular objectives, when the feasible solutions are independent sets of a p-system. With the exception of additive valuation functions, no mechanisms were known for this setting prior to our work. Finally, we provide lower bounds suggesting that, when one cares about non-trivial approximation guaran
Developments in Multi-Agent Fair Allocation
Fairness is becoming an increasingly important concern when designing
markets, allocation procedures, and computer systems. I survey some recent
developments in the field of multi-agent fair allocation
The Limitations of Optimization from Samples
In this paper we consider the following question: can we optimize objective
functions from the training data we use to learn them? We formalize this
question through a novel framework we call optimization from samples (OPS). In
OPS, we are given sampled values of a function drawn from some distribution and
the objective is to optimize the function under some constraint.
While there are interesting classes of functions that can be optimized from
samples, our main result is an impossibility. We show that there are classes of
functions which are statistically learnable and optimizable, but for which no
reasonable approximation for optimization from samples is achievable. In
particular, our main result shows that there is no constant factor
approximation for maximizing coverage functions under a cardinality constraint
using polynomially-many samples drawn from any distribution.
We also show tight approximation guarantees for maximization under a
cardinality constraint of several interesting classes of functions including
unit-demand, additive, and general monotone submodular functions, as well as a
constant factor approximation for monotone submodular functions with bounded
curvature
Honest signaling in zero-sum games is hard, and lying is even harder
We prove that, assuming the exponential time hypothesis, finding an
\epsilon-approximately optimal symmetric signaling scheme in a two-player
zero-sum game requires quasi-polynomial time. This is tight by [Cheng et al.,
FOCS'15] and resolves an open question of [Dughmi, FOCS'14]. We also prove that
finding a multiplicative approximation is NP-hard.
We also introduce a new model where a dishonest signaler may publicly commit
to use one scheme, but post signals according to a different scheme. For this
model, we prove that even finding a (1-2^{-n})-approximately optimal scheme is
NP-hard
Budget-Feasible Mechanism Design for Non-monotone Submodular Objectives: Offline and Online
The framework of budget-feasible mechanism design studies procurement auctions where the auctioneer (buyer) aims to maximize his valuation function subject to a hard budget constraint. We study the problem of designing truthful mechanisms that have good approximation guarantees and never pay the participating agents (sellers) more than the budget. We focus on the case of general (non-monotone) submodular valuation functions and derive the first truthful, budget-feasible, and O(1)-approximation mechanisms that run in polynomial time in the value query model, for both offline and online auctions. Prior to our work, the only O(1)-approximation mechanism known for non-monotone submodular objectives required an exponential number of value queries. At the heart of our approach lies a novel greedy algorithm for non-monotone submodular maximization under a knapsack constraint. Our algorithm builds two candidate solutions simultaneously (to achieve a good approximation), yet ensures that agents cannot jump from one solution to the other (to implicitly enforce truthfulness). The fact that in our mechanism the agents are not ordered according to their marginal value per cost allows us to appropriately adapt these ideas to the online setting as well. To further illustrate the applicability of our approach, we also consider the case where additional feasibility constraints are present, for example, at most k agents can be selected. We obtain O(p)-approximation mechanisms for both monotone and non-monotone submodular objectives, when the feasible solutions are independent sets of a p-system. With the exception of additive valuation functions, no mechanisms were known for this setting prior to our work. Finally, we provide lower bounds suggesting that, when one cares about nontrivial approximation guarantees in polynomial time, our results are, asymptotically, the best possible
- …