We consider an extension to classic position auctions in which sponsored creatives are embedded within AI-generated content rather than shown in predefined slots. Leveraging advanced LLM technologies, it becomes viable to seamlessly integrate sponsored creatives with AI content and accurately estimate the context-aware benefits of differing insertion positions. However, this approach introduces novel challenges; substitution effects require rigorous treatment compared to standard position auction settings, where slots are independent of each other.

Generative AI (GenAI) will have significant impact on content creation platforms. In this paper, we study the dynamic competition between a GenAI and a human contributor. Unlike the human, the GenAI's content only improves when more contents are created by the human over time; however, GenAI has the advantage of generating content at a lower cost. We study the algorithmic problem in this dynamic competition model about how the human contributor can maximize her utility when competing against the GenAI for content generation over a set of topics. In time-sensitive content domains (e.g., news or pop music creation) where contents' value diminishes over time, we show that there is no polynomial time algorithm for finding the human's optimal (dynamic) strategy, unless the randomized exponential time hypothesis is false. Fortunately, we are able to design a polynomial time algorithm that naturally cycles between myopically optimizing over a short time window and pausing and provably guarantees an approximation ratio of 1/2 . We then turn to time-insensitive content domains where contents do not lose their value (e.g., contents on history facts). Interestingly, we show that this setting permits a polynomial time algorithm that maximizes the human's utility in the long run. Finally, we conduct simulations that demonstrate the advantage of our algorithms in comparison to a collection of baselines.

We consider the problem of maximizing a submodular function with access to a _noisy_ value oracle for the function instead of an exact value oracle. Similar to prior work, we assume that the noisy oracle is persistent in that multiple calls to the oracle for a specific set always return the same value. In this model, Hassidim and Singer (2017) design a $(1-1/e)$-approximation algorithm for monotone submodular maximization subject to a cardinality constraint, and Huang et al (2022) design a $(1-1/e)/2$-approximation algorithm for monotone submodular maximization subject to any arbitrary matroid constraint. In this paper, we design a meta-algorithm that allows us to take any "robust" algorithm for exact submodular maximization as a black box and transform it into an algorithm for the noisy setting while retaining the approximation guarantee. By using the meta-algorithm with the measured continuous greedy algorithm, we obtain a $(1-1/e)$-approximation (resp. $1/e$-approximation) for monotone (resp. non-monotone) submodular maximization subject to a matroid constraint under noise. Furthermore, by using the meta-algorithm with the double greedy algorithm, we obtain a $1/2$-approximation for unconstrained (non-monotone) submodular maximization under noise.

We consider the problem of bidding in online advertising, where an advertiser aims to maximize value while adhering to budget and Return-on-Spend (RoS) constraints. Unlike prior work that assumes knowledge of the value generated by winning each impression (e.g., conversions), we address the more realistic setting where the advertiser must simultaneously learn the optimal bidding strategy and the value of each impression opportunity. This introduces a challenging exploration-exploitation dilemma: the advertiser must balance exploring different bids to estimate impression values with exploiting current knowledge to bid effectively. To address this, we propose a novel Upper Confidence Bound (UCB)-style algorithm that carefully manages this trade-off. Via a rigorous theoretical analysis, we prove that our algorithm achieves Õ(₲T log(|B|T) ) regret and constraint violation, where T is the number of bidding rounds and B is the domain of possible bids. This establishes the first optimal regret and constraint violation bounds for bidding in the online setting with unknown impression values. Moreover, our algorithm is computationally efficient and simple to implement. We validate our theoretical findings through experiments on synthetic data, demonstrating that our algorithm exhibits strong empirical performance compared to existing approaches.

We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of $\frac{e}{e-1}$, and provide a $\frac{4e}{e-1}$-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.

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.

Budget pacing is a popular service that has been offered by major internet advertising platforms since their inception. In the past few years, autobidding products that provide real-time bidding as a service to advertisers have seen a prominent rise in adoption. A popular autobidding stategy is value maximization subject to return-on-spend (ROS) constraints. For historical or business reasons, the systems that govern these two services, namely budget pacing and ROS pacing, are not necessarily always a single unified and coordinated entity that optimizes a global objective subject to both constraints. The purpose of this work is to theoretically and empirically compare algorithms with different degrees of coordination between these two pacing systems. In particular, we compare (a) a fully-decoupled sequential algorithm; (b) a minimally-coupled min-pacing algorithm; (c) a fully-coupled dual-based algorithm. Our main contribution is to theoretically analyze the min-pacing algorithm and show that it attains similar guarantees to the fully-coupled canonical dual-based algorithm. On the other hand, we show that the sequential algorithm, even though appealing by virtue of being fully decoupled, could badly violate the constraints. We validate our theoretical findings empirically by showing that the min-pacing algorithm performs almost as well as the canonical dual-based algorithm on a semi-synthetic dataset that was generated from a large online advertising platform's auction data.

We study an auction setting in which bidders bid for placement of their content within a summary generated by a large language model (LLM), e.g., an ad auction in which the display is a summary paragraph of multiple ads. This generalizes the classic ad settings such as position auctions to an LLM generated setting, which allows us to handle general display formats. We propose a novel factorized framework in which an auction module and an LLM module work together via a prediction model to provide welfare maximizing summary outputs in an incentive compatible manner. We provide a theoretical analysis of this framework and synthetic experiments to demonstrate the feasibility and validity of the system together with welfare comparisons.

We propose a new Markov Decision Process (MDP) model for ad auctions to capture the user response to the quality of ads, with the objective of maximizing the long-term discounted revenue. By incorporating user response, our model takes into consideration all three parties involved in the auction (advertiser, auctioneer, and user). The state of the user is modeled as a user-specific click-through rate (CTR) with the CTR changing in the next round according to the set of ads shown to the user in the current round. We characterize the optimal mechanism for this MDP as a Myerson's auction with a notion of modified virtual value, which relies on the value distribution of the advertiser, the current user state, and the future impact of showing the ad to the user. Leveraging this characterization, we design a sample-efficient and computationally-efficient algorithm which outputs an approximately optimal policy that requires only sample access to the true MDP and the value distributions of the bidders. Finally, we propose a simple mechanism built upon second price auctions with personalized reserve prices and show it can achieve a constant-factor approximation to the optimal long term discounted revenue.

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981, but more than 40 years later, a full analytical understanding of the optimal design still remains elusive for settings with two or more items. In this work, we initiate the exploration of the use of tools from deep learning for the automated design of optimal auctions. We model an auction as a multi-layer neural network, frame optimal auction design as a constrained learning problem, and show how it can be solved using standard machine learning pipelines. In addition to providing generalization bounds, we present extensive experimental results, recovering essentially all known solutions that come from the theoretical analysis of optimal auction design problems and obtaining novel mechanisms for settings in which the optimal mechanism is unknown.

In this work, we investigate the online learning problem of revenue maximization in ad auctions, where the seller needs to learn the click-through rates (CTRs) of each ad candidate and charge the price of the winner through a pay-per-click manner. We focus on two models of the advertisers’ strategic behaviors. First, we assume that the advertiser is completely myopic; i.e. in each round, they aim to maximize their utility only for the current round. In this setting, we develop an online mechanism based on upper-confidence bounds that achieves a tight $O(\sqrt{T})$ regret in the worst-case and negative regret when the values are static across all the auctions and there is a gap between the highest expected value (i.e. value multiplied by their CTR) and second highest expected value ad. Next, we assume that the advertiser is non-myopic and cares about their long term utility. This setting is much more complex since an advertiser is incentivized to influence the mechanism by bidding strategically in earlier rounds. In this setting, we provide an algorithm to achieve negative regret for the static valuation setting (with a positive gap), which is in sharp contrast with the prior work that shows $O(T^{2/3})$ regret when the valuation is generated by adversary.

Standard contextual bandit problem assumes that all the relevant contexts are observed before the algorithm chooses an arm. This modeling paradigm, while useful, often falls short when dealing with problems in which additional valuable contexts can be observed after arm selection. For example, content recommendation platforms like Youtube, Instagram, Tiktok receive much additional features about a user's reward after the user clicks a content (e.g., how long the user stayed, what is the user's watch speed, etc.). To improve online learning efficiency in these applications, we study a novel contextual bandit problem with post-serving contexts and design a new algorithm, poLinUCB, that achieves tight regret under standard assumptions. Core to our technical proof is a robustified and generalized version of the well-known Elliptical Potential Lemma (EPL), which can accommodate noise in data. Such robustification is necessary for tackling our problem, though we believe it could also be of general interest. Extensive empirical tests on both synthetic and real-world datasets demonstrate the significant benefit of utilitzing post-serving contexts as well as the superior performance of our algorithm over the state-of-the-art approaches.

In this work, we investigate the problem of how to bid in repeated contextual first price auctions for a single learner (the bidder). Concretely, at each time t, the learner receives a context and decides the bid based on historical information and xt. We assume that the maximum bid of all the others follows a linear model, i.e., mt = ⟨α0, xt⟩ + zt, where is unknown to the learner and zt is randomly sampled from a noise distribution with log-concave density. In this work, we consider both binary feedback (the learner can only observe whether she wins or not) and full information feedback (the learner can observe mt) models of the learner. For binary feedback, when the noise distribution is (partially) known, we propose a bidding algorithm that achieves at most regret, where Δ is a constant reserve in first price auctions.1 For the full information feedback with unknown noise distribution, we provide an algorithm that achieves regret at most . Our approach combines an estimator for log-concave density functions and the Maximum Likelihood Estimation (MLE) method to learn the noise distribution and linear weight α0 simultaneously. We complement our results with a lower bound result such that any bidding policy in a broad class must achieve regret at least , even when the learner receives the full information feedback and is known.

We study online auto-bidding algorithms for a single advertiser maximizing value under the Return-on-Spend (RoS) constraint, quantifying performance in terms of regret relative to the optimal offline solution that knows all queries a priori. We contribute a simple online algorithm that achieves near-optimal regret in expectation while always respecting the RoS constraint when the input queries are i.i.d. samples from some distribution. Integrating our results with [9] achieves near-optimal regret under both RoS and fixed budget constraints. Our algorithm uses the primal-dual framework with online mirror descent (OMD) for the dual updates, and the analysis utilizes new insights into the gradient structure.

One of the central problems in auction design is developing an incentive-compatible mechanism that maximizes the auctioneer’s expected revenue. While theoretical approaches have encountered bottlenecks in multi-item auctions, recently, there has been much progress on finding the optimal mechanism through deep learning. However, these works either focus on a fixed set of bidders and items, or restrict the auction to be symmetric. In this work, we overcome such limitations by factoring public contextual information of bidders and items into the auction learning framework. We propose $\mathtt{CITransNet}$, a context-integrated transformer-based neural network for optimal auction design, which maintains permutation-equivariance over bids and contexts while being able to find asymmetric solutions. We show by extensive experiments that $\mathtt{CITransNet}$ can recover the known optimal solutions in single-item settings, outperform strong baselines in multi-item auctions, and generalize well to cases other than those in training.

Incrementality, which measures the causal effect of showing an ad to a potential customer (e.g. a user in an internet platform) versus not, is a central object for advertisers in online advertising platforms. This paper investigates the problem of how an advertiser can learn to optimize the bidding sequence in an online manner \emph{without} knowing the incrementality parameters in advance. We formulate the offline version of this problem as a specially structured episodic Markov Decision Process (MDP) and then, for its online learning counterpart, propose a novel reinforcement learning (RL) algorithm with regret at most $\widetilde{O}(H^2\sqrt{T})$, which depends on the number of rounds $H$ and number of episodes $T$, but does not depend on the number of actions (i.e., possible bids). A fundamental difference between our learning problem from standard RL problems is that the realized reward feedback from conversion incrementality is \emph{mixed} and \emph{delayed}. To handle this difficulty we propose and analyze a novel pairwise moment-matching algorithm to learn the conversion incrementality, which we believe is of independent interest.

In today's economy, it becomes important for Internet platforms to consider the sequential information design problem to align its long term interest with incentives of the gig service providers (e.g., drivers, hosts). This paper proposes a novel model of sequential information design, namely the Markov persuasion processes (MPPs), in which a sender, with informational advantage, seeks to persuade a stream of myopic receivers to take actions that maximize the sender's cumulative utilities in a finite horizon Markovian environment with varying prior and utility functions. Planning in MPPs thus faces the unique challenge in finding a signaling policy that is simultaneously persuasive to the myopic receivers and inducing the optimal long-term cumulative utilities of the sender. Nevertheless, in the population level where the model is known, it turns out that we can efficiently determine the optimal (resp. ε-optimal) policy with finite (resp. infinite) states and outcomes, through a modified formulation of the Bellman equation that additionally takes persuasiveness into consideration.

The connection between games and no-regret algorithms has been widely studied in the literature. A fundamental result is that when all players play no-regret strategies, this produces a sequence of actions whose time-average is a coarse-correlated equilibrium of the game. However, much less is known about equilibrium selection in the case that multiple equilibria exist. In this work, we study the convergence of no-regret bidding algorithms in auctions. Besides being of theoretical interest, bidding dynamics in auctions is an important question from a practical viewpoint as well. We study the repeated game between bidders in which a single item is sold at each time step and the bidder's value is drawn from an unknown distribution. We show that if the bidders use any mean-based learning rule then the bidders converge with high probability to the truthful pure Nash Equilibrium in a second price auction, in VCG auction in the multi-slot setting and to the Bayesian Nash equilibrium in a first price auction. We note mean-based algorithms cover a wide variety of known no-regret algorithms such as Exp3, UCB, \epsilon-Greedy etc. Also, we analyze the convergence of the individual iterates produced by such learning algorithms, as opposed to the time-average of the sequence. Our experiments corroborate our theoretical findings and also find a similar convergence when we use other strategies such as Deep Q-Learning.

The display advertising industry has recently transitioned from second- to first-price auctions as its primary mechanism for ad allocation and pricing. In light of this, publishers need to re-evaluate and optimize their auction parameters, notably reserve prices. In this paper, we propose a gradient-based algorithm to adaptively update and optimize reserve prices based on estimates of bidders’ responsiveness to experimental shocks in reserves. Our key innovation is to draw on the inherent structure of the revenue objective in order to reduce the variance of gradient estimates and improve convergence rates in both theory and practice. We show that revenue in a first-price auction can be usefully decomposed into a \emph{demand} component and a \emph{bidding} component, and introduce techniques to reduce the variance of each component. We characterize the bias-variance trade-offs of these techniques and validate the performance of our proposed algorithm through experiments on synthetic data and real display ad auctions data from a major ad exchange.

Motivated by economic applications such as recommender systems, we study the behavior of stochastic bandits algorithms under \emph{strategic behavior} conducted by rational actors, i.e., the arms. Each arm is a \emph{self-interested} strategic player who can modify its own reward whenever pulled, subject to a cross-period budget constraint, in order to maximize its own expected number of times of being pulled. We analyze the robustness of three popular bandit algorithms: UCB, $\varepsilon$-Greedy, and Thompson Sampling. We prove that all three algorithms achieve a regret upper bound $\mathcal{O}(\max \{ B, K\ln T\})$ where $B$ is the total budget across arms, $K$ is the total number of arms and $T$ is the running time of the algorithms. This regret guarantee holds for \emph{arbitrary adaptive} manipulation strategy of arms. Our second set of main results shows that this regret bound is \emph{tight}— in fact, for UCB, it is tight even when we restrict the arms’ manipulation strategies to form a \emph{Nash equilibrium}. We do so by characterizing the Nash equilibrium of the game induced by arms’ strategic manipulations and show a regret lower bound of $\Omega(\max \{ B, K\ln T\})$ at the equilibrium.

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981. Even after 30-40 years of intense research the problem remains unsolved for seemingly simple multi-bidder, multi-item settings. In this work, we initiate the exploration of the use of tools from deep learning for the automated design of optimal auctions. We model an auction as a multi-layer neural network, frame optimal auction design as a constrained learning problem, and show how it can be solved using standard pipelines. We prove generalization bounds and present extensive experiments, recovering essentially all known analytical solutions for multi-item settings, and obtaining novel mechanisms for settings in which the optimal mechanism is unknown.

In this paper we investigate the problem of measuring end-to-end Incentive Compatibility (IC) regret given black-box access to an auction mechanism. Our goal is to 1) compute an estimate for IC regret in an auction, 2) provide a measure of certainty around the estimate of IC regret, and 3) minimize the time it takes to arrive at an accurate estimate. We consider two main problems, with different informational assumptions: In the advertiser problem the goal is to measure IC regret for some known valuation v, while in the more general demand-side platform (DSP) problem we wish to determine the worst-case IC regret over all possible valuations. The problems are naturally phrased in an online learning model and we design algorithms for both problems. We give an online learning algorithm where for the advertiser problem the error of determining IC shrinks as (where B is the finite set of bids, T is the number of time steps, and n is number of auctions per time step), and for the DSP problem it shrinks as . For the DSP problem, we also consider stronger IC regret estimation and extend our algorithm to achieve better IC regret error. We validate the theoretical results using simulations with Generalized Second Price (GSP) auctions, which are known to not be incentive compatible and thus have strictly positive IC regret.

We address online learning in complex auction settings, such as sponsored search auctions, where the value of the bidder is unknown to her, evolving in an arbitrary manner and observed only if the bidder wins an allocation. We leverage the structure of the utility of the bidder and the partial feedback that bidders typically receive in auctions, in order to provide algorithms with regret rates against the best fixed bid in hindsight, that are exponentially faster in convergence in terms of dependence on the action space, than what would have been derived by applying a generic bandit algorithm and almost equivalent to what would have been achieved in the full information setting. Our results are enabled by analyzing a new online learning setting with outcome-based feedback, which generalizes learning with feedback graphs. We provide an online learning algorithm for this setting, of independent interest, with regret that grows only logarithmically with the number of actions and linearly only in the number of potential outcomes (the latter being very small in most auction settings). Last but not least, we show that our algorithm outperforms the bandit approach experimentally and that this performance is robust to dropping some of our theoretical assumptions or introducing noise in the feedback that the bidder receives.