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Book ; Online: Description Complexity of Regular Distributions

Leme, Renato Paes / Sivan, Balasubramanian / Teng, Yifeng / Worah, Pratik

2023

Abstract: Myerson's regularity condition of a distribution is a standard assumption in economics. In this paper, we study the complexity of describing a regular distribution within a small statistical distance. Our main result is that $\tilde{\Theta}{(\epsilon^{-0. ...

Abstract	Myerson's regularity condition of a distribution is a standard assumption in economics. In this paper, we study the complexity of describing a regular distribution within a small statistical distance. Our main result is that $\tilde{\Theta}{(\epsilon^{-0.5})}$ bits are necessary and sufficient to describe a regular distribution with support $[0,1]$ within $\epsilon$ Levy distance. We prove this by showing that we can learn the regular distribution approximately with $\tilde{O}(\epsilon^{-0.5})$ queries to the cumulative density function. As a corollary, we show that the pricing query complexity to learn the class of regular distribution with support $[0,1]$ within $\epsilon$ Levy distance is $\tilde{\Theta}{(\epsilon^{-2.5})}$. To learn the mixture of two regular distributions, $\tilde{\Theta}(\epsilon^{-3})$ pricing queries are required.
Keywords	Computer Science - Computer Science and Game Theory ; Economics - Theoretical Economics
Publishing date	2023-05-09
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: U-Calibration

Kleinberg, Robert / Leme, Renato Paes / Schneider, Jon / Teng, Yifeng

Forecasting for an Unknown Agent

2023

Abstract: We consider the problem of evaluating forecasts of binary events whose predictions are consumed by rational agents who take an action in response to a prediction, but whose utility is unknown to the forecaster. We show that optimizing forecasts for a ... ...

Abstract	We consider the problem of evaluating forecasts of binary events whose predictions are consumed by rational agents who take an action in response to a prediction, but whose utility is unknown to the forecaster. We show that optimizing forecasts for a single scoring rule (e.g., the Brier score) cannot guarantee low regret for all possible agents. In contrast, forecasts that are well-calibrated guarantee that all agents incur sublinear regret. However, calibration is not a necessary criterion here (it is possible for miscalibrated forecasts to provide good regret guarantees for all possible agents), and calibrated forecasting procedures have provably worse convergence rates than forecasting procedures targeting a single scoring rule. Motivated by this, we present a new metric for evaluating forecasts that we call U-calibration, equal to the maximal regret of the sequence of forecasts when evaluated under any bounded scoring rule. We show that sublinear U-calibration error is a necessary and sufficient condition for all agents to achieve sublinear regret guarantees. We additionally demonstrate how to compute the U-calibration error efficiently and provide an online algorithm that achieves $O(\sqrt{T})$ U-calibration error (on par with optimal rates for optimizing for a single scoring rule, and bypassing lower bounds for the traditionally calibrated learning procedures). Finally, we discuss generalizations to the multiclass prediction setting. Comment: Accepted for presentation at the Conference on Learning Theory (COLT) 2023
Keywords	Computer Science - Machine Learning ; Computer Science - Computer Science and Game Theory
Subject code	006
Publishing date	2023-06-30
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Buy-Many Mechanisms for Many Unit-Demand Buyers

Chawla, Shuchi / Rezvan, Rojin / Teng, Yifeng / Tzamos, Christos

2022

Abstract: A recent line of research has established a novel desideratum for designing approximately-revenue-optimal multi-item mechanisms, namely the buy-many constraint. Under this constraint, prices for different allocations made by the mechanism must be ... ...

Abstract	A recent line of research has established a novel desideratum for designing approximately-revenue-optimal multi-item mechanisms, namely the buy-many constraint. Under this constraint, prices for different allocations made by the mechanism must be subadditive implying that the price of a bundle cannot exceed the sum of prices of individual items it contains. This natural constraint has enabled several positive results in multi-item mechanism design bypassing well-established impossibility results. Our work addresses a main open question from this literature involving the design of buy-many mechanisms for multiple buyers. Our main result is that a simple sequential item pricing mechanism with buyer-specific prices can achieve an $O(\log m)$ approximation to the revenue of any buy-many mechanism when all buyers have unit-demand preferences over $m$ items. This is the best possible as it directly matches the previous results for the single-buyer setting where no simple mechanism can obtain a better approximation. Our result applies in full generality: even though there are many alternative ways buy-many mechanisms can be defined for multi-buyer settings, our result captures all of them at the same time. We achieve this by directly competing with a more permissive upper-bound on the buy-many revenue, obtained via an ex-ante relaxation.
Keywords	Computer Science - Computer Science and Game Theory
Subject code	005
Publishing date	2022-04-04
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Worst-Case Welfare of Item Pricing in the Tollbooth Problem

Tan, Zihan / Teng, Yifeng / Zhao, Mingfei

2021

Abstract: We study the worst-case welfare of item pricing in the \emph{tollbooth problem}. The problem was first introduced by Guruswami et al, and is a special case of the combinatorial auction in which (i) each of the $m$ items in the auction is an edge of some ... ...

Abstract	We study the worst-case welfare of item pricing in the \emph{tollbooth problem}. The problem was first introduced by Guruswami et al, and is a special case of the combinatorial auction in which (i) each of the $m$ items in the auction is an edge of some underlying graph; and (ii) each of the $n$ buyers is single-minded and only interested in buying all edges of a single path. We consider the competitive ratio between the hindsight optimal welfare and the optimal worst-case welfare among all item-pricing mechanisms, when the order of the arriving buyers is adversarial. We assume that buyers own the \emph{tie-breaking} power, i.e. they can choose whether or not to buy the demand path at 0 utility. We prove a tight competitive ratio of $3/2$ when the underlying graph is a single path (also known as the \emph{highway} problem), whereas item-pricing can achieve the hindsight optimal if the seller is allowed to choose a proper tie-breaking rule to maximize the welfare. Moreover, we prove an $O(1)$ upper bound of competitive ratio when the underlying graph is a tree. For general graphs, we prove an $\Omega(m^{1/8})$ lower bound of the competitive ratio. We show that an $m^{\Omega(1)}$ competitive ratio is unavoidable even if the graph is a grid, or if the capacity of every edge is augmented by a constant factor $c$. The results hold even if the seller has tie-breaking power.
Keywords	Computer Science - Computer Science and Game Theory ; Computer Science - Discrete Mathematics ; Computer Science - Data Structures and Algorithms
Subject code	511
Publishing date	2021-07-12
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Prophet Secretary Against the Online Optimal

Dütting, Paul / Gergatsouli, Evangelia / Rezvan, Rojin / Teng, Yifeng / Tsigonias-Dimitriadis, Alexandros

2023

Abstract: We study the prophet secretary problem, a well-studied variant of the classic prophet inequality, where values are drawn from independent known distributions but arrive in uniformly random order. Upon seeing a value at each step, the decision-maker has ... ...

Abstract	We study the prophet secretary problem, a well-studied variant of the classic prophet inequality, where values are drawn from independent known distributions but arrive in uniformly random order. Upon seeing a value at each step, the decision-maker has to either select it and stop or irrevocably discard it. Traditionally, the chosen benchmark is the expected reward of the prophet, who knows all the values in advance and can always select the maximum one. %% In this work, we study the prophet secretary problem against a less pessimistic but equally well-motivated benchmark; the \emph{online} optimal. Here, the main goal is to find polynomial-time algorithms that guarantee near-optimal expected reward. As a warm-up, we present a quasi-polynomial time approximation scheme (QPTAS) achieving a $(1-\e)$-approximation in $O(n^{\text{poly} \log n\cdot f(\e)})$ time through careful discretization and non-trivial bundling processes. Using the toolbox developed for the QPTAS, coupled with a novel \emph{frontloading} technique that enables us to reduce the number of decisions we need to make, we are able to remove the dependence on $n$ in the exponent and obtain a polynomial time approximation scheme (PTAS) for this problem.
Keywords	Computer Science - Computer Science and Game Theory
Subject code	000
Publishing date	2023-05-18
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Learning Thresholds with Latent Values and Censored Feedback

Zhang, Jiahao / Lin, Tao / Zheng, Weiqiang / Feng, Zhe / Teng, Yifeng / Deng, Xiaotie

2023

Abstract: In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward $g(\gamma, v)$ depends on the proposed threshold $\gamma$ and latent value $v$ and it can be $only$ achieved if the threshold is lower than ... ...

Abstract	In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward $g(\gamma, v)$ depends on the proposed threshold $\gamma$ and latent value $v$ and it can be $only$ achieved if the threshold is lower than or equal to the unknown latent value. This problem has broad applications in practical scenarios, e.g., reserve price optimization in online auctions, online task assignments in crowdsourcing, setting recruiting bars in hiring, etc. We first characterize the query complexity of learning a threshold with the expected reward at most $\epsilon$ smaller than the optimum and prove that the number of queries needed can be infinitely large even when $g(\gamma, v)$ is monotone with respect to both $\gamma$ and $v$. On the positive side, we provide a tight query complexity $\tilde{\Theta}(1/\epsilon^3)$ when $g$ is monotone and the CDF of value distribution is Lipschitz. Moreover, we show a tight $\tilde{\Theta}(1/\epsilon^3)$ query complexity can be achieved as long as $g$ satisfies one-sided Lipschitzness, which provides a complete characterization for this problem. Finally, we extend this model to an online learning setting and demonstrate a tight $\Theta(T^{2/3})$ regret bound using continuous-arm bandit techniques and the aforementioned query complexity results. Comment: 18 pages
Keywords	Computer Science - Machine Learning ; Computer Science - Computer Science and Game Theory
Subject code	006 ; 005
Publishing date	2023-12-07
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Buy-many mechanisms are not much better than item pricing

Chawla, Shuchi / Teng, Yifeng / Tzamos, Christos

2019

Abstract: Multi-item mechanisms can be very complex offering many different bundles to the buyer that could even be randomized. Such complexity is thought to be necessary as the revenue gaps between randomized and deterministic mechanisms, or deterministic and ... ...

Abstract	Multi-item mechanisms can be very complex offering many different bundles to the buyer that could even be randomized. Such complexity is thought to be necessary as the revenue gaps between randomized and deterministic mechanisms, or deterministic and simple mechanisms are huge even for additive valuations. We challenge this conventional belief by showing that these large gaps can only happen in restricted situations. These are situations where the mechanism overcharges a buyer for a bundle while selling individual items at much lower prices. Arguably this is impractical in many settings because the buyer can break his order into smaller pieces paying a much lower price overall. Our main result is that if the buyer is allowed to purchase as many (randomized) bundles as he pleases, the revenue of any multi-item mechanism is at most O(logn) times the revenue achievable by item pricing, where n is the number of items. This holds in the most general setting possible, with an arbitrarily correlated distribution of buyer types and arbitrary valuations. We also show that this result is tight in a very strong sense. Any family of mechanisms of subexponential description complexity cannot achieve better than logarithmic approximation even against the best deterministic mechanism and even for additive valuations. In contrast, item pricing that has linear description complexity matches this bound against randomized mechanisms.
Keywords	Computer Science - Computer Science and Game Theory
Subject code	005
Publishing date	2019-02-26
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Revenue Maximization for Query Pricing

Chawla, Shuchi / Deep, Shaleen / Koutris, Paraschos / Teng, Yifeng

2019

Abstract: Buying and selling of data online has increased substantially over the last few years. Several frameworks have already been proposed that study query pricing in theory and practice. The key guiding principle in these works is the notion of {\em arbitrage- ...

Abstract	Buying and selling of data online has increased substantially over the last few years. Several frameworks have already been proposed that study query pricing in theory and practice. The key guiding principle in these works is the notion of {\em arbitrage-freeness} where the broker can set different prices for different queries made to the dataset, but must ensure that the pricing function does not provide the buyers with opportunities for arbitrage. However, little is known about revenue maximization aspect of query pricing. In this paper, we study the problem faced by a broker selling access to data with the goal of maximizing her revenue. We show that this problem can be formulated as a revenue maximization problem with single-minded buyers and unlimited supply, for which several approximation algorithms are known. We perform an extensive empirical evaluation of the performance of several pricing algorithms for the query pricing problem on real-world instances. In addition to previously known approximation algorithms, we propose several new heuristics and analyze them both theoretically and experimentally. Our experiments show that algorithms with the best theoretical bounds are not necessarily the best empirically. We identify algorithms and heuristics that are both fast and also provide consistently good performance when valuations are drawn from a variety of distributions. Comment: To appear in PVLDB; version 2 with some cosmetic changes
Keywords	Computer Science - Databases
Subject code	005
Publishing date	2019-09-02
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Online Allocation and Display Ads Optimization with Surplus Supply

Abolhassani, Melika / Esfandiari, Hossein / Nazari, Yasamin / Sivan, Balasubramanian / Teng, Yifeng / Thomas, Creighton

2021

Abstract: In this work, we study a scenario where a publisher seeks to maximize its total revenue across two sales channels: guaranteed contracts that promise to deliver a certain number of impressions to the advertisers, and spot demands through an Ad Exchange. ... ...

Abstract	In this work, we study a scenario where a publisher seeks to maximize its total revenue across two sales channels: guaranteed contracts that promise to deliver a certain number of impressions to the advertisers, and spot demands through an Ad Exchange. On the one hand, if a guaranteed contract is not fully delivered, it incurs a penalty for the publisher. On the other hand, the publisher might be able to sell an impression at a high price in the Ad Exchange. How does a publisher maximize its total revenue as a sum of the revenue from the Ad Exchange and the loss from the under-delivery penalty? We study this problem parameterized by \emph{supply factor $f$}: a notion we introduce that, intuitively, captures the number of times a publisher can satisfy all its guaranteed contracts given its inventory supply. In this work we present a fast simple deterministic algorithm with the optimal competitive ratio. The algorithm and the optimal competitive ratio are a function of the supply factor, penalty, and the distribution of the bids in the Ad Exchange. Beyond the yield optimization problem, classic online allocation problems such as online bipartite matching of [Karp-Vazirani-Vazirani '90] and its vertex-weighted variant of [Aggarwal et al. '11] can be studied in the presence of the additional supply guaranteed by the supply factor. We show that a supply factor of $f$ improves the approximation factors from $1-1/e$ to $f-fe^{-1/f}$. Our approximation factor is tight and approaches $1$ as $f \to \infty$.
Keywords	Computer Science - Computer Science and Game Theory ; Computer Science - Data Structures and Algorithms
Subject code	070
Publishing date	2021-07-14
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Pandora's Box with Correlations

Chawla, Shuchi / Gergatsouli, Evangelia / Teng, Yifeng / Tzamos, Christos / Zhang, Ruimin

Learning and Approximation

2019

Abstract: The Pandora's Box problem and its extensions capture optimization problems with stochastic input where the algorithm can obtain instantiations of input random variables at some cost. To our knowledge, all previous work on this class of problems assumes ... ...

Abstract	The Pandora's Box problem and its extensions capture optimization problems with stochastic input where the algorithm can obtain instantiations of input random variables at some cost. To our knowledge, all previous work on this class of problems assumes that different random variables in the input are distributed independently. As such it does not capture many real-world settings. In this paper, we provide the first approximation algorithms for Pandora's Box-type problems with correlations. We assume that the algorithm has access to samples drawn from the joint distribution on input. Algorithms for these problems must determine an order in which to probe random variables, as well as when to stop and return the best solution found so far. In general, an optimal algorithm may make both decisions adaptively based on instantiations observed previously. Such fully adaptive (FA) strategies cannot be efficiently approximated to within any sublinear factor with sample access. We therefore focus on the simpler objective of approximating partially adaptive (PA) strategies that probe random variables in a fixed predetermined order but decide when to stop based on the instantiations observed. We consider a number of different feasibility constraints and provide simple PA strategies that are approximately optimal with respect to the best PA strategy for each case. All of our algorithms have polynomial sample complexity. We further show that our results are tight within constant factors: better factors cannot be achieved even using the full power of FA strategies.
Keywords	Computer Science - Data Structures and Algorithms
Subject code	006
Publishing date	2019-11-05
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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