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DOI: 10.4230/LIPIcs.ITCS.2023.52

Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence

Authors: Jason Gaitonde, Yingkai Li, Bar Light, Brendan Lucier, and Aleksandrs Slivkins

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract

Online advertising via auctions increasingly dominates the marketing landscape. A typical advertiser may participate in thousands of auctions each day with bids tailored to a variety of signals about user demographics and intent. These auctions are strategically linked through a global budget constraint. To help address the difficulty of bidding, many major online platforms now provide automated budget management via a flexible approach called budget pacing: rather than bidding directly, an advertiser specifies a global budget target and a maximum willingness-to-pay for different types of advertising opportunities. The specified maximums are then scaled down (or "paced") by a multiplier so that the realized total spend matches the target budget. These automated bidders are now near-universally adopted across all mature advertising platforms, raising pressing questions about market outcomes that arise when advertisers use budget pacing simultaneously. In this paper we study the aggregate welfare and individual regret guarantees of dynamic pacing algorithms in repeated auctions with budgets. We show that when agents simultaneously use a natural form of gradient-based pacing, the liquid welfare obtained over the course of the dynamics is at least half the optimal liquid welfare obtainable by any allocation rule, matching the best possible bound for static auctions even in pure Nash equilibria [Aggarwal et al., WINE 2019; Babaioff et al., ITCS 2021]. In contrast to prior work, these results hold without requiring convergence of the dynamics, circumventing known computational obstacles of finding equilibria [Chen et al., EC 2021]. Our result is robust to the correlation structure among agents' valuations and holds for any core auction, a broad class that includes first-price, second-price, and GSP auctions. We complement the aggregate guarantees by showing that an agent using such pacing algorithms achieves an O(T^{3/4}) regret relative to the value obtained by the best fixed pacing multiplier in hindsight in stochastic bidding environments. Compared to past work, this result applies to more general auctions and extends to adversarial settings with respect to dynamic regret.

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Jason Gaitonde, Yingkai Li, Bar Light, Brendan Lucier, and Aleksandrs Slivkins. Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, p. 52:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gaitonde_et_al:LIPIcs.ITCS.2023.52,
  author =	{Gaitonde, Jason and Li, Yingkai and Light, Bar and Lucier, Brendan and Slivkins, Aleksandrs},
  title =	{{Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{52:1--52:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.52},
  URN =		{urn:nbn:de:0030-drops-175557},
  doi =		{10.4230/LIPIcs.ITCS.2023.52},
  annote =	{Keywords: repeated auctions with budgets, pacing, learning in auctions}
}

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DOI: 10.4230/LIPIcs.ITCS.2018.48

Competing Bandits: Learning Under Competition

Authors: Yishay Mansour, Aleksandrs Slivkins, and Zhiwei Steven Wu

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract

Most modern systems strive to learn from interactions with users, and many engage in exploration: making potentially suboptimal choices for the sake of acquiring new information. We initiate a study of the interplay between exploration and competition--how such systems balance the exploration for learning and the competition for users. Here the users play three distinct roles: they are customers that generate revenue, they are sources of data for learning, and they are self-interested agents which choose among the competing systems. In our model, we consider competition between two multi-armed bandit algorithms faced with the same bandit instance. Users arrive one by one and choose among the two algorithms, so that each algorithm makes progress if and only if it is chosen. We ask whether and to what extent competition incentivizes the adoption of better bandit algorithms. We investigate this issue for several models of user response, as we vary the degree of rationality and competitiveness in the model. Our findings are closely related to the "competition vs. innovation" relationship, a well-studied theme in economics.

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Yishay Mansour, Aleksandrs Slivkins, and Zhiwei Steven Wu. Competing Bandits: Learning Under Competition. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 48:1-48:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{mansour_et_al:LIPIcs.ITCS.2018.48,
  author =	{Mansour, Yishay and Slivkins, Aleksandrs and Wu, Zhiwei Steven},
  title =	{{Competing Bandits: Learning Under Competition}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{48:1--48:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.48},
  URN =		{urn:nbn:de:0030-drops-83341},
  doi =		{10.4230/LIPIcs.ITCS.2018.48},
  annote =	{Keywords: machine learning, game theory, competition, exploration, rationality}
}

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Documents authored by Slivkins, Aleksandrs

Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence

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Competing Bandits: Learning Under Competition

Abstract

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