7 research outputs found
Statistical Inference and A/B Testing for First-Price Pacing Equilibria
We initiate the study of statistical inference and A/B testing for
first-price pacing equilibria (FPPE). The FPPE model captures the dynamics
resulting from large-scale first-price auction markets where buyers use
pacing-based budget management. Such markets arise in the context of internet
advertising, where budgets are prevalent.
We propose a statistical framework for the FPPE model, in which a limit FPPE
with a continuum of items models the long-run steady-state behavior of the
auction platform, and an observable FPPE consisting of a finite number of items
provides the data to estimate primitives of the limit FPPE, such as revenue,
Nash social welfare (a fair metric of efficiency), and other parameters of
interest. We develop central limit theorems and asymptotically valid confidence
intervals. Furthermore, we establish the asymptotic local minimax optimality of
our estimators. We then show that the theory can be used for conducting
statistically valid A/B testing on auction platforms. Numerical simulations
verify our central limit theorems, and empirical coverage rates for our
confidence intervals agree with our theory.Comment: - fix referenc
Statistical Inference for Fisher Market Equilibrium
Statistical inference under market equilibrium effects has attracted
increasing attention recently. In this paper we focus on the specific case of
linear Fisher markets. They have been widely use in fair resource allocation of
food/blood donations and budget management in large-scale Internet ad auctions.
In resource allocation, it is crucial to quantify the variability of the
resource received by the agents (such as blood banks and food banks) in
addition to fairness and efficiency properties of the systems. For ad auction
markets, it is important to establish statistical properties of the platform's
revenues in addition to their expected values. To this end, we propose a
statistical framework based on the concept of infinite-dimensional Fisher
markets. In our framework, we observe a market formed by a finite number of
items sampled from an underlying distribution (the "observed market") and aim
to infer several important equilibrium quantities of the underlying long-run
market. These equilibrium quantities include individual utilities, social
welfare, and pacing multipliers. Through the lens of sample average
approximation (SSA), we derive a collection of statistical results and show
that the observed market provides useful statistical information of the
long-run market. In other words, the equilibrium quantities of the observed
market converge to the true ones of the long-run market with strong statistical
guarantees. These include consistency, finite sample bounds, asymptotics, and
confidence. As an extension, we discuss revenue inference in quasilinear Fisher
markets
Greedy-Based Online Fair Allocation with Adversarial Input: Enabling Best-of-Many-Worlds Guarantees
We study an online allocation problem with sequentially arriving items and
adversarially chosen agent values, with the goal of balancing fairness and
efficiency. Our goal is to study the performance of algorithms that achieve
strong guarantees under other input models such as stochastic inputs, in order
to achieve robust guarantees against a variety of inputs. To that end, we study
the PACE (Pacing According to Current Estimated utility) algorithm, an existing
algorithm designed for stochastic input. We show that in the equal-budgets
case, PACE is equivalent to the integral greedy algorithm. We go on to show
that with natural restrictions on the adversarial input model, both integral
greedy allocation and PACE have asymptotically bounded multiplicative envy as
well as competitive ratio for Nash welfare, with the multiplicative factors
either constant or with optimal order dependence on the number of agents. This
completes a "best-of-many-worlds" guarantee for PACE, since past work showed
that PACE achieves guarantees for stationary and stochastic-but-non-stationary
input models
Local AdaGrad-Type Algorithm for Stochastic Convex-Concave Minimax Problems
Large scale convex-concave minimax problems arise in numerous applications,
including game theory, robust training, and training of generative adversarial
networks. Despite their wide applicability, solving such problems efficiently
and effectively is challenging in the presence of large amounts of data using
existing stochastic minimax methods. We study a class of stochastic minimax
methods and develop a communication-efficient distributed stochastic
extragradient algorithm, LocalAdaSEG, with an adaptive learning rate suitable
for solving convex-concave minimax problem in the Parameter-Server model.
LocalAdaSEG has three main features: (i) periodic communication strategy
reduces the communication cost between workers and the server; (ii) an adaptive
learning rate that is computed locally and allows for tuning-free
implementation; and (iii) theoretically, a nearly linear speed-up with respect
to the dominant variance term, arising from estimation of the stochastic
gradient, is proven in both the smooth and nonsmooth convex-concave settings.
LocalAdaSEG is used to solve a stochastic bilinear game, and train generative
adversarial network. We compare LocalAdaSEG against several existing optimizers
for minimax problems and demonstrate its efficacy through several experiments
in both the homogeneous and heterogeneous settings.Comment: 24 page