# Jon Schneider

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Auto-bidding and Auctions in Online Advertising: A Survey

Ashwinkumar Badanidiyuru Varadaraja

Christopher Liaw

Haihao (Sean) Lu

Andres Perlroth

Georgios Piliouras

Ariel Schvartzman

Kelly Spendlove

Hanrui Zhang

Mingfei Zhao

ACM SIGecom Exchanges, 22 (2024)

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In this survey, we summarize recent developments in research fueled by the growing adoption of automated bidding strategies in online advertising. We explore the challenges and opportunities that have arisen as markets embrace this autobidding and cover a range of topics in this area, including bidding algorithms, equilibrium analysis and efficiency of common auction formats, and optimal auction design.
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Complex Dynamics in Autobidding Systems

Georgios Piliouras

Kelly Spendlove

Proceedings of the 25th ACM Conference on Economics and Computation (2024)

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It has become the default in markets such as ad auctions for participants to bid in an auction through automated bidding agents (autobidders) which adjust bids over time to satisfy return-over-spend constraints. Despite the prominence of such systems for the internet economy, their resulting dynamical behavior is still not well understood. Although one might hope that such relatively simple systems would typically converge to the equilibria of their underlying auctions, we provide a plethora of results that show the emergence of complex behavior, such as bi-stability, periodic orbits and quasi periodicity. We empirically observe how the market structure (expressed as motifs) qualitatively affects the behavior of the dynamics. We complement it with theoretical results showing that autobidding systems can simulate both linear dynamical systems as well logical boolean gates.
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Contextual Recommendations and Low-Regret Cutting-Plane Algorithms

Guru Prashanth Guruganesh

NeurIPS (2021)

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We consider the following variant of contextual linear bandits motivated by routing applications in navigational engines and recommendation systems. We wish to learn a hidden $d$-dimensional value $w^*$. Every round, we are presented with a subset $\mathcal{X}_t \subseteq \mathbb{R}^d$ of possible actions. If we choose (i.e. recommend to the user) action $x_t$, we obtain utility $\langle x_t, w^* \rangle$ but only learn the identity of the best action $\arg\max_{x \in \X_t} \langle x, w^* \rangle$.
We design algorithms for this problem which achieve regret $O(d\log T)$ and $\exp(O(d \log d))$. To accomplish this, we design novel cutting-plane algorithms with low “regret” -- the total distance between the true point $w^*$ and the hyperplanes the separation oracle returns.
We also consider the variant where we are allowed to provide a list of several recommendations. In this variant, we give an algorithm with $O(d^2 \log d)$ regret and list size $\poly(d)$. Finally, we construct nearly tight algorithms for a weaker variant of this problem where the learner only learns the identity of an action that is better than the recommendation. Our results rely on new algorithmic techniques in convex geometry (including a variant of Steiner’s formula for the centroid of a convex set) which may be of independent interest.
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Strategizing against No-regret Learners

Advances in Neural Information Processing Systems (2019), pp. 1579-1587

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How should a player who repeatedly plays a game against a no-regret learner strategize to maximize his utility? We study this question and show that under some mild assumptions, the player can always guarantee himself a utility of at least what he would get in a Stackelberg equilibrium of the game. When the no-regret learner has only two actions, we show that the player cannot get any higher utility than the Stackelberg equilibrium utility. But when the no-regret learner has more than two actions and plays a mean-based no-regret strategy, we show that the player can get strictly higher than the Stackelberg equilibrium utility. We provide a characterization of the optimal game-play for the player against a mean-based no-regret learner as a solution to a control problem. When the no-regret learner's strategy also guarantees him a no-swap regret, we show that the player cannot get anything higher than a Stackelberg equilibrium utility.
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Prior-Free Dynamic Auctions with Low Regret Buyers

Advances in Neural Information Processing Systems (2019), pp. 4803-4813

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We study the problem of how to repeatedly sell to a buyer running a no-regret, mean-based algorithm. Previous work (Braverman et al., EC '18) shows that it is possible to design effective mechanisms in such a setting that extract almost all of the economic surplus, but these mechanisms require the buyer's values each round to be drawn iid from a fixed distribution. In this paper, we do away with this assumption and consider the {\it prior-free setting} where the buyer's value each round is chosen adversarially (possibly adaptively).
We show that even in this prior-free setting, it is possible to extract a $(1-\varepsilon)$-approximation of the full economic surplus for any $\varepsilon > 0$. The menu complexity of our mechanism (the number of options offered to a buyer in any round) scales independently of the number of rounds $T$ and polynomially in $\varepsilon$. We show that this is optimal up to a polynomial factor; any mechanism achieving this approximation factor, even when values are drawn stochastically, requires menu complexity at least $\Omega(1/\varepsilon)$.
Finally, we examine what is possible when we constrain our mechanism to a natural auction format where overbidding is dominated. Braverman et al. show that even when values are drawn from a known stochastic distribution supported on $[1/H, 1]$, it is impossible in general to extract more than $O(\log\log H / \log H)$ of the economic surplus. We show how to achieve the same approximation factor in the {\it prior-independent} setting (where the distribution is unknown to the seller), and an approximation factor of $O(1 / \log H)$ in the prior-free setting.
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