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.

In the secretary problem, a set of secretary candidates arrive in a uniformly random order and reveal their values one by one. A company, who can only hire one candidate and hopes to maximize the expected value of its hire, needs to make irrevocable online decisions about whether to hire the current candidate. The classical framework of evaluating a policy is to compute its worst-case competitive ratio against the optimal solution in hindsight, and there the best policy -- the ''1/e law'' -- has a competitive ratio of 1/e. We propose an alternative evaluation framework through the lens of regret -- the worst-case additive difference between the optimal hindsight solution and the expected performance of the policy, assuming that each value is normalized between 0 and 1. The 1/e law for the classical framework has a regret of 1 - 1/e ≈ 0.632; by contrast, we show that the class of ''pricing curves'' algorithms can guarantee a regret of at most 1/4 = 0.25 (which is tight within the class), and the class of ''best-only pricing curves'' algorithms can guarantee a regret of at most 0.190 (with a lower bound of 0.171). In addition, we show that in general, no policy can give a regret guarantee better than 0.152. Finally, we discuss other objectives in our regret-minimization framework.

The *turnstile* continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data analysis, both the length of the stream $T$ and the size of the universe $|\mathcal{U}|$ from which data come can be extremely large. This motivates the study of private algorithms in the turnstile setting using space sublinear in both $T$ and $|\mathcal{U}|$. In this paper, we give the first sublinear space differentially private algorithms for the fundamental problems of counting distinct elements in the turnstile streaming model. Our algorithm achieves, on arbitrary streams, $O_{\eta}(T^{1/3})$ space and additive error, and a $(1+\eta)$-relative approximation for all $\eta \in (0,1)$. Our result significantly improves upon the space requirements of the state-of-the-art algorithms for this problem, which is linear, approaching the known $\Omega(T^{1/4})$ additive error lower bound for arbitrary streams. Moreover, when a bound $W$ on the number of times an item appears in the stream is known, our algorithm provides $O_{\eta}(\sqrt{W})$ additive error, using $O_{\eta}(\sqrt{W})$ space. This additive error asymptotically matches that of prior work which required instead linear space. Our results address an open question posed by Jain et al. about designing low-memory mechanisms for this problem. We complement this results with a space lower bound for this problem, which shows that any algorithm that uses similar techniques must use space $\Omega(T^{1/3})$.

The performance of a model trained with noisy labels is often improved by simply *retraining* the model with its *own predicted hard labels* (i.e., $1$/$0$ labels). Yet, a detailed theoretical characterization of this phenomenon is lacking. In this paper, we theoretically analyze retraining in a linearly separable binary classification setting with randomly corrupted labels given to us and prove that retraining can improve the population accuracy obtained by initially training with the given (noisy) labels. To the best of our knowledge, this is the first such theoretical result. Retraining finds application in improving training with local label differential privacy (DP), which involves training with noisy labels. We empirically show that retraining selectively on the samples for which the predicted label matches the given label significantly improves label DP training at no extra privacy cost; we call this consensus-based retraining. For example, when training ResNet-18 on CIFAR-100 with $\epsilon=3$ label DP, we obtain more than $6$% improvement in accuracy with consensus-based retraining.

We study the social efficiency of bilateral trade between a seller and a buyer. In the classical Bayesian setting, the celebrated Myerson-Satterthwaite impossibility theorem states that no Bayesian incentive-compatible, individually rational, and budget-balanced mechanism can achieve full efficiency. As a counterpoint, Deng, Mao, Sivan, and Wang (STOC 2022) show that if pricing power is delegated to the right person (either the seller or the buyer), the resulting mechanism can guarantee at least a constant fraction of the ideal (yet unattainable) gains from trade.

The recent increasing adoption of autobidding has inspired the growing interest in analyzing the performance of classic mechanism with value-maximizing autobidders both theoretically and empirically. It is known that optimal welfare can be obtained in first-price auctions if autobidders are restricted to uniform bid-scaling and the price of anarchy is $2$ when non-uniform bid-scaling strategies are allowed. In this paper, we provide a fine-grained price of anarchy analysis for non-uniform bid-scaling strategies in first-price auctions, demonstrating the reason why more powerful (individual) non-uniform bid-scaling strategies may lead to worse (aggregated) performance in social welfare. Our theoretical results match recent empirical findings that a higher level of non-uniform bid-scaling leads to lower welfare performance in first-price auctions.

We study the price of anarchy of first-price auctions in the autobidding world, where bidders can be either utility maximizers (i.e., traditional bidders) or value maximizers (i.e., autobidders). We show that with autobidders only, the price of anarchy of first-price auctions is $1/2$, and with both kinds of bidders, the price of anarchy degrades to about $0.457$ (the precise number is given by an optimization). These results complement the recent result by [Jin and Lu, 2022] showing that the price of anarchy of first-price auctions with traditional bidders is $1 - 1/e^2$. We further investigate a setting where the seller can utilize machine-learned advice to improve the efficiency of the auctions. There, we show that as the accuracy of the advice increases, the price of anarchy improves smoothly from about $0.457$ to $1$.

Motivated by the increased adoption of autobidding algorithms in internet advertising markets, we study the design of optimal mechanisms for selling an item to a value-maximizing buyer with a return-on-spend constraint. The buyer's values and target ratio in the return-on-spend constraint are private. We restrict attention to deterministic sequential screening mechanisms that can be implemented as a menu of two-part tariffs. The main result of this paper is to provide a characterization of an optimal mechanism. Surprisingly, we show that the optimal mechanism does not require target screening, i.e., offering a single two-part tariff is optimal for the seller. The optimal mechanism is a subsidized two-part tariff that provides a lump-sum subsidy to the buyer to encourage participation and then charges a fixed unit price for each item sold. The seller's problem is a challenging non-linear mechanism design problem, and a key technical contribution of our work is to provide a novel approach to analyzing non-linear pricing contracts for constrained buyers. Our results have valuable implications for advertising platforms seeking to personalize pricing decisions based on advertisers' characteristics.

We study the price of anarchy of the generalized second-price auction where bidders are value maximizers (i.e., autobidders). We show that in general the price of anarchy can be as bad as 0. For comparison, the price of anarchy of running VCG is 1/2 in the autobidding world. We further show a fined-grained price of anarchy with respect to the discount factors (i.e., the ratios of click probabilities between lower slots and the highest slot in each auction) in the generalized second-price auction, which highlights the qualitative relation between the smoothness of the discount factors and the efficiency of the generalized second-price auction.

In recent years, the growing adoption of autobidding has motivated the study of auction design with value-maximizing auto-bidders. It is known that under mild assumptions, uniform bid-scaling is an optimal bidding strategy in truthful auctions, e.g., Vickrey-Clarke-Groves auction (VCG), and the price of anarchy for VCG is 2. However, for other auction formats like First-Price Auction (FPA) and Generalized Second-Price auction (GSP), uniform bid-scaling may not be an optimal bidding strategy, and bidders have incentives to deviate to adopt strategies with non-uniform bid-scaling. Moreover, FPA can achieve optimal welfare if restricted to uniform bid-scaling, while its price of anarchy becomes 2 when non-uniform bid-scaling strategies are allowed.

The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass through the stream and using as little space as possible. Motivated by the importance of data privacy, we develop differentially private streaming algorithms under the continual release setting, where the union of outputs of the algorithm at every timestamp must be differentially private. Specifically, we study the fundamental $\ell_p$ $(p\in [0,+\infty))$ frequency moment estimation problem under this setting, and give an $\varepsilon$-DP algorithm that achieves $(1+η)$-relative approximation $(\forall η\in(0,1))$ with $\mathrm{poly}\log(Tn)$ additive error and uses $\mathrm{poly}\log(Tn)\cdot \max(1, n^{1-2/p})$ space, where $T$ is the length of the stream and $n$ is the size of the universe of elements. Our space is near optimal up to poly-logarithmic factors even in the non-private setting. To obtain our results, we first reduce several primitives under the differentially private continual release model, such as counting distinct elements, heavy hitters and counting low frequency elements, to the simpler, counting/summing problems in the same setting. Based on these primitives, we develop a differentially private continual release level set estimation approach to address the $\ell_p$ frequency moment estimation problem. We also provide a simple extension of our results to the harder sliding window model, where the statistics must be maintained over the past $W$ data items.

In a typical optimization problem, the task is to pick one of a number of options with the lowest cost or the highest value. In practice, these cost/value quantities are often not accurately known: they can come from physical measurements with imperfect tools, estimations of machine learning algorithms, or observations from differentially private mechanisms. In many of these situations, the cost/value quantities are noisy, but with quantifiable noise distributions. To take these noise distributions into account, one approach is to assume a prior distribution for the values, use it to build a posterior, and then apply standard stochastic optimization to pick a solution. However, in many practical applications, such prior distributions may not be available. In this paper, we study such scenarios using a regret minimization model.

A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time). The buyer will remain in the market for a period of time T, and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing-curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each point of time and let the buyer pick her utility maximizing time to buy, are revenue-optimal among a much broader class of sequential lottery mechanisms: namely, mechanisms that allow the seller to post a menu of lotteries at each point of time cannot get any higher revenue than pricing curves. We also show that the even broader class of mechanisms that allow the menu of lotteries to be adaptively set, can earn strictly higher revenue than that of pricing curves, and the revenue gap can be as big as the support size of the buyer's value distribution. * The full version of the paper can be accessed at https://arxiv.org/abs/2106.02149.

We study autobidding ad auctions with user costs, where each bidder is value-maximizing subject to a return-over-investment (ROI) constraint, and the seller aims to maximize the social welfare taking into consideration the user’s cost of viewing an ad. We show that in the worst case, the approximation ratio of social welfare by running the vanilla VCG auctions with user costs could as bad as 0. To improve the performance of VCG, We propose a new variant of VCG based on properly chosen cost multipliers, and prove that there exist auction-dependent and bidder-dependent cost multipliers that guarantee approximation ratios of 1/2 and 1/4 respectively in terms of the social welfare.

We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case of a one-round communication protocol. We define message complexity corresponding to the minimum number of interactive rounds necessary to achieve the best possible outcome. Our main result is that for bilateral trade, agents don't stop talking until they reach an efficient outcome: Either agents achieve an efficient allocation in finitely many rounds of communication; or the optimal communication protocol has infinite number of rounds. We show an important class of bilateral trade settings where efficient allocation is achievable with a small number of rounds of communication.

We study the design of revenue-maximizing mechanisms for value-maximizing agents with budget constraints. Agents have return-on-spend constraints requiring a minimum amount of value per unit of payment made and budget constraints limiting their total payments. The agents' only private information are the minimum admissible ratios on the return-on-spend constraint, referred to as the target ratios.

We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer’s value weakly exceeds seller’s cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism that obtains a 1/8.23 ≈ 0.121 fraction of the first-best.

We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally differentially private protocols as straightforward corollaries of results from communication complexity. In particular, we (1) use a communication lower bound for the hidden layers problem to prove an exponential sample complexity separation between sequentially and fully interactive locally private protocols, and (2) use a communication lower bound for the pointer chasing problem to prove an exponential sample complexity separation between k -round and ( k+1 )-round sequentially interactive locally private protocols, for every k .

In classic auction theory, reserve prices are known to be effective for improving revenue for the auctioneer against quasi-linear utility maximizing bidders. The introduction of reserve prices, however, usually do not help improve total welfare of the auctioneer and the bidders. In this paper, we focus on value maximizing bidders with return on spend constraints---a paradigm that has drawn considerable attention recently as more advertisers adopt auto-bidding algorithms in advertising platforms---and show that the introduction of reserve prices has a novel impact on the market. Namely, by choosing reserve prices appropriately the auctioneer can improve not only the total revenue but also the total welfare. Our results also demonstrate that reserve prices are robust to bidder types, i.e., reserve prices work well for different bidder types, such as value maximizers and utility maximizers, without using bidder type information. We generalize these results for a variety of auction mechanisms such as VCG, GSP, and first-price auctions. Moreover, we show how to combine these results with additive boosts to improve the welfare of the outcomes of the auction further. Finally, we complement our theoretical observations with an empirical study confirming the effectiveness of these ideas using data from online advertising auctions.

Internet advertisers are increasingly adopting automated bidders to buy advertising opportunities. Automated bidders simplify the procurement process by allowing advertisers to specify their goals and then bidding on their behalf in the auctions that are used to sell advertising slots. One popular goal adopted by advertisers is to maximize their clicks (or conversions) subject to a return on spend (RoS) constraint, which imposes that the ratio of total value to total spend is greater than a target ratio specified by the advertisers. The emergence of automated bidders brings into question whether the standard mechanisms used to sell ads are still effective in this new landscape. Thus motivated, in this paper, we study the problem of characterizing optimal mechanisms for selling an item to one of multiple agents with return on spend constraints when either the values or target ratios are private. We consider two objectives for the agents: value maximization, which is becoming the prevalent objective in advertising markets, and utility maximization, which is the de facto paradigm in economic theory. Our goal is to understand the impact of the agents' private information and their objectives on the seller's revenue, and determine whether the first-best revenue, which is the optimal revenue when all the private information is public, is achievable. We show that first-best revenue is achievable for value-maximizing buyers when either the target ratio or the values are private, but not when both are private. In the case of utility-maximizing buyers, first-best is never achievable and we characterize revenue-maximizing mechanisms.

Bidding dashboards are used in online marketplaces to aid a bidder in computing good bidding strategies, particularly when the auction used by the marketplace is constrained to have the winners-pay-bid payment format. A dashboard predicts the outcome a bidder can expect to get at each possible bid. To convince a bidder to best respond to the information published in a dashboard, a dashboard mechanism should ensure either (a) that best responding maximizes the bidder's utility (a weaker requirement) or (b) that the mechanism implements the outcome published in the dashboard (a stronger requirement that subsumes (a)). Recent work by Hartline et al. EC'19 formalized the notion of dashboard mechanisms and designed winners-pay-bid mechanisms that guaranteed epsilon-optimal utility (an epsilon-approximate version of (a)), but not (b). I.e., the mechanism could end up implementing arbitrarily different outcomes from what was promised. While this guarantee is sufficient from a purely technical perspective, it is far from enough in the real world: it is hard to convince bidders to best respond to information which could be arbitrarily inaccurate, regardless of the theoretical promise of near-optimality. In this paper we study guaranteed dashboard mechanisms, namely, ones that are guaranteed to implement what they publish, and obtain good welfare. We study this question in a repeated auction setting for general single-dimensional valuations and give tight characterizations of the loss in welfare as a function of natural parameters upper bounding the difference in valuation profile across the rounds. In particular, we give three different characterizations, bounding the loss in welfare in terms of the 0 norm, 1 norm and infinite norm of difference in valuation profile across rounds. All the characterizations generalize at least up to matroid feasibility constraints, and the infinite norm characterization extends to general downward-closed feasibility constraints. We bring to bear different techniques for each of these characterizations, including connections to differential privacy and online convex optimizations.

In the shuffle model of differential privacy, data-holding users send randomized messages to a secure shuffler, the shuffler permutes the messages, and the resulting collection of messages must be differentially private with regard to user data. In the pan-private model, an algorithm processes a stream of data while maintaining an internal state that is differentially private with regard to the stream data. We give evidence connecting these two apparently different models. Our results focus on robustly shuffle private protocols, whose privacy guarantees are not greatly affected by malicious users. First, we give robustly shuffle private protocols and upper bounds for counting distinct elements and uniformity testing. Second, we use pan-private lower bounds to prove robustly shuffle private lower bounds for both problems. Focusing on the dependence on the domain size k, we find that robust shuffle privacy and pan-privacy have additive error for counting distinct elements. For uniformity testing, we give a robustly shuffle private protocol with sample complexity Õ(k2/3) and show that an Ω(k2/3) dependence is necessary in a specific parameter regime. Finally, we show that this connection is useful in both directions: we give a pan-private adaptation of recent work on shuffle private histograms and use it to recover further separations between pan-privacy and interactive local privacy.

Auto-bidding has become one of the main options for bidding in online advertisements, in which advertisers only need to specify high-level objectives and leave the complex task of bidding to auto-bidders. In this paper, we propose a family of auctions with boosts to improve welfare in auto-bidding environments with both return on ad spend constraints and budget constraints. Our empirical results validate our theoretical findings and show that both the welfare and revenue can be improved by selecting the weight of the boosts properly.

A centrally differentially private algorithm maps raw data to differentially private outputs. In contrast, a locally differentially private algorithm may only access data through public interaction with data holders, and this interaction must be a differentially private function of the data. We study the intermediate model of \emph{pan-privacy}. Unlike a locally private algorithm, a pan-private algorithm receives data in the clear. Unlike a centrally private algorithm, the algorithm receives data one element at a time and must maintain a differentially private internal state while processing this stream. First, we show that pan-privacy against multiple intrusions on the internal state is equivalent to sequentially interactive local privacy. Next, we contextualize pan-privacy against a single intrusion by analyzing the sample complexity of uniformity testing over domain $[k]$. Focusing on the dependence on $k$, centrally private uniformity testing has sample complexity $\Theta(\sqrt{k})$, while noninteractive locally private uniformity testing has sample complexity $\Theta(k)$. We show that the sample complexity of pan-private uniformity testing is $\Theta(k^{2/3})$. By a new $\Omega(k)$ lower bound for the sequentially interactive setting, we also separate pan-private from sequentially interactive locally private and multi-intrusion pan-private uniformity testing.

A differentially private algorithm guarantees that the input of a single user won’t significantly change the output distribution of the algorithm. When a user contributes more data points, more information can be collected to improve the algorithm’s performance. But at the same time, more noise might need to be added to the algorithm in order to keep the algorithm differentially private and this might hurt the algorithm’s performance. Amin et al. (2019) initiates the study on bounding user contributions and proposes a very natural algorithm which limits the number of samples each user can contribute by a threshold. For a better trade-off between utility and privacy guarantee, we propose a method which smoothly bounds user contributions by setting appropriate weights on data points and apply it to estimating the mean/quantiles, linear regression, and empirical risk minimization. We show that our algorithm provably outperforms the sample limiting algorithm. We conclude with experimental evaluations which validate our theoretical results.

We study the design of rating systems that incentivize (more) efficient social learning among self-interested agents. Agents arrive sequentially and are presented with a set of possible actions, each of which yields a positive reward with an unknown probability. A disclosure policy sends messages about the rewards of previously-chosen actions to arriving agents. These messages can alter agents' incentives towards exploration, taking potentially sub-optimal actions for the sake of learning more about their rewards. Prior work achieves much progress with disclosure policies that merely recommend an action to each user, without any other supporting information, and sometimes recommend exploratory actions. All this work relies heavily on standard, yet very strong rationality assumptions. However, these assumptions are quite problematic in the context of the motivating applications: recommendation systems such as Yelp, Amazon, or Netflix, and macthing markets such as AirBnB. It is very unclear whether users would know and understand a complicated disclosure policy announced by the principal, let alone trust the principal to faithfully implement it. (The principal may deviate from the announced policy either intentionally, or due to insufficient information about the users, or because of bugs in implementation.) Even if the users understand the policy and trust that it was implemented as claimed, they might not react to it rationally, particularly given the lack of supporting information and the possibility of being singled out for exploration. For example, users may find such disclosure policies unacceptable and leave the system.

We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally differentially private protocols as straightforward corollaries of results from communication complexity. In particular, we 1) use a communication lower bound for the hidden layers problem to prove an exponential sample complexity separation between sequentially and fully interactive locally private protocols, and 2) use a communication lower bound for the pointer chasing problem to prove an exponential sample complexity separation between k-round and (k + 1)-round sequentially interactive locally private protocols, for every k.

We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We restrict our attention to algorithms with a constant number of rounds $r$ and try to minimize the sample complexity, i.e. the number of comparisons. When the comparisons are noiseless, we characterize how the optimal sample complexity depends on the number of rounds (up to a polylogarithmic factor for general $r$ and up to a constant factor for $r=1$ or 2). In particular, the sample complexity is $\Theta(n^2)$ for $r=1$, $\Theta(n\sqrt{k} + n^{4/3})$ for $r=2$ and $\tilde{\Theta}\left(n^{2/r} k^{(r-1)/r} + n\right)$ for $r \geq 3$. We extend our results of sorted top-$k$ to the noisy case where each comparison is correct with probability $2/3$. When $r=1$ or 2, we show that the sample complexity gets an extra $\Theta(\log(k))$ factor when we transition from the noiseless case to the noisy case. We also prove new results for top-$k$ and sorting in the noisy case. We believe our techniques can be generally useful for understanding the trade-off between round complexities and sample complexities of rank aggregation problems.

We study a strategic version of the multi-armed bandit problem, where each arm is an individual strategic agent and we, the principal, pull one arm each round. When pulled, the arm receives some private reward $v_a$ and can choose an amount $x_a$ to pass on to the principal (keeping $v_a-x_a$ for itself). All non-pulled arms get reward $0$. Each strategic arm tries to maximize its own utility over the course of $T$ rounds. Our goal is to design an algorithm for the principal incentivizing these arms to pass on as much of their private rewards as possible. When private rewards are stochastically drawn each round ($v_a^t \leftarrow D_a$), we show that: \begin{itemize} \item Algorithms that perform well in the classic adversarial multi-armed bandit setting necessarily perform poorly: For all algorithms that guarantee low regret in an adversarial setting, there exist distributions $D_1,\ldots,D_k$ and an $o(T)$-approximate Nash equilibrium for the arms where the principal receives reward $o(T)$. \item There exists an algorithm for the principal that induces a game among the arms where each arm has a dominant strategy. Moreover, for every $o(T)$-approximate Nash equilibrium, the principal receives expected reward $\mu’T - o(T)$, where $\mu’$ is the second-largest of the means $\mathbb{E}[D_{a}]$. This algorithm maintains its guarantee if the arms are non-strategic ($x_a = v_a$), and also if there is a mix of strategic and non-strategic arms. \end{itemize}

We study the power of interactivity in local differential privacy. First, we focus on the difference between fully interactive and sequentially interactive protocols. Sequentially interactive protocols may query users adaptively in sequence, but they cannot return to previously queried users. The vast majority of existing lower bounds for local differential privacy apply only to sequentially interactive protocols, and before this paper it was not known whether fully interactive protocols were more powerful. We resolve this question. First, we classify locally private protocols by their compositionality, the multiplicative factor by which the sum of a protocol's single-round privacy parameters exceeds its overall privacy guarantee. We then show how to efficiently transform any fully interactive compositional protocol into an equivalent sequentially interactive protocol with a blowup in sample complexity linear in this compositionality. Next, we show that our reduction is tight by exhibiting a family of problems such that any sequentially interactive protocol requires this blowup in sample complexity over a fully interactive compositional protocol. We then turn our attention to hypothesis testing problems. We show that for a large class of compound hypothesis testing problems - which include all simple hypothesis testing problems as a special case - a simple noninteractive test is optimal among the class of all (possibly fully interactive) tests.

Motivated by settings in which predictive models may be required to be non-discriminatory with respect to certain attributes (such as race), but even collecting the sensitive attribute may be forbidden or restricted, we initiate the study of fair learning under the constraint of differential privacy. Our first algorithm is a private implementation of the equalized odds post-processing approach of (Hardt et al., 2016). This algorithm is appealingly simple, but must be able to use protected group membership explicitly at test time, which can be viewed as a form of “disparate treatment”. Our second algorithm is a differentially private version of the oracle-efficient in-processing approach of (Agarwal et al., 2018) which is more complex but need not have access to protected group membership at test time. We identify new tradeoffs between fairness, accuracy, and privacy that emerge only when requiring all three properties, and show that these tradeoffs can be milder if group membership may be used at test time. We conclude with a brief experimental evaluation.

We study a basic private estimation problem: each of n users draws a single i.i.d. sample from an unknown Gaussian distribution N(\mu,\sigma^2), and the goal is to estimate \mu while guaranteeing local differential privacy for each user. As minimizing the number of rounds of interaction is important in the local setting, we provide adaptive two-round solutions and nonadaptive one-round solutions to this problem. We match these upper bounds with an information-theoretic lower bound showing that our accuracy guarantees are tight up to logarithmic factors for all sequentially interactive locally private protocols.

It is common in recommendation systems that users both consume and produce information as they make strategic choices under uncertainty. While a social planner would balance “exploration” and “exploitation” using a multi-armed bandit algorithm, users' incentives may tilt this balance in favor of exploitation. We consider Bayesian Exploration: a simple model in which the recommendation system (the “principal”) controls the information flow to the users (the “agents”) and strives to incentivize exploration via information asymmetry. A single round of this model is a version of a well-known “Bayesian Persuasion game” from [24]. We allow heterogeneous users, relaxing a major assumption from prior work that users have the same preferences from one time step to another. The goal is now to learn the best personalized recommendations. One particular challenge is that it may be impossible to incentivize some of the user types to take some of the actions, no matter what the principal does or how much time she has. We consider several versions of the model, depending on whether and when the user types are reported to the principal, and design a near-optimal “recommendation policy” for each version. We also investigate how the model choice and the diversity of user types impact the set of actions that can possibly be “explored” by each type.

In consumer search, there is a set of items. An agent has a prior over her value for each item and can pay a cost to learn the instantiation of her value. After exploring a subset of items, the agent chooses one and obtains a payoff equal to its value minus the search cost. We consider a sequential model of consumer search in which agents' values are correlated and each agent updates her priors based on the exploration of past agents before performing her search. Specifically, we assume the value is the sum of a common-value component, called the quality, and a subjective score. Fixing the variance of the total value, we say a population is more diverse if the subjective score has a larger variance. We ask how diversity impacts average utility. We show that intermediate diversity levels yield significantly higher social utility than the extreme cases of no diversity (when agents under-explore) or full diversity (when agents are unable to learn from each other) and quantify how the impact of the diversity level changes depending on the time spent searching.

We investigate the problem of learning a Lipschitz function from binary feedback. In this problem, a learner is trying to learn a Lipschitz function $f:[0,1]^d \rightarrow [0,1]$ over the course of $T$ rounds. On round $t$, an adversary provides the learner with an input $x_t$, the learner submits a guess $y_t$ for $f(x_t)$, and learns whether $y_t > f(x_t)$ or $y_t \leq f(x_t)$. The learner's goal is to minimize their total loss $\sum_t\ell(f(x_t), y_t)$ (for some loss function $\ell$). The problem is motivated by \textit{contextual dynamic pricing}, where a firm must sell a stream of differentiated products to a collection of buyers with non-linear valuations for the items and observes only whether the item was sold or not at the posted price. For the symmetric loss $\ell(f(x_t), y_t) = \vert f(x_t) - y_t \vert$, we provide an algorithm for this problem achieving total loss $O(\log T)$ when $d=1$ and $O(T^{(d-1)/d})$ when $d>1$, and show that both bounds are tight (up to a factor of $\sqrt{\log T}$). For the pricing loss function $\ell(f(x_t), y_t) = f(x_t) - y_t {\bf 1}\{y_t \leq f(x_t)\}$ we show a regret bound of $O(T^{d/(d+1)})$ and show that this bound is tight. We present improved bounds in the special case of a population of linear buyers.

We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution D in every round). Prior work assumes that the buyer is fully rational and will perfectly reason about how their bids today affect the seller's decisions tomorrow. In this work we initiate a different direction: the buyer simply runs a no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically: - If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), then the seller can extract expected revenue arbitrarily close to the expected welfare. This auction is independent of the buyer's valuation D , but somewhat unnatural as it is sometimes in the buyer's interest to overbid. - There exists a learning algorithm A such that if the buyer bids according to A then the optimal strategy for the seller is simply to post the Myerson reserve for D every round. - If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), but the seller is restricted to "natural" auction formats where overbidding is dominated (e.g. Generalized First-Price or Generalized Second-Price), then the optimal strategy for the seller is a pay-your-bid format with decreasing reserves over time. Moreover, the seller's optimal achievable revenue is characterized by a linear program, and can be unboundedly better than the best truthful auction yet simultaneously unboundedly worse than the expected welfare.

We consider the following communication problem: Alice and Bob each have some valuation functions υ1(·) and υ2(·) over subsets of m items, and their goal is to partition the items into S, in a way that maximizes the welfare, . We study both the allocation problem, which asks for a welfare-maximizing partition and the decision problem, which asks whether or not there exists a partition guaranteeing certain welfare, for binary XOS valuations. For interactive protocols with poly(m) communication, a tight 3/4-approximation is known for both [29, 23]. For interactive protocols, the allocation problem is provably harder than the decision problem: any solution to the allocation problem implies a solution to the decision problem with one additional round and log m additional bits of communication via a trivial reduction. Surprisingly, the allocation problem is provably easier for simultaneous protocols. Specifically, we show: There exists a simultaneous, randomized protocol with polynomial communication that selects a partition whose expected welfare is at least 3/4 of the optimum. This matches the guarantee of the best interactive, randomized protocol with polynomial communication. For all ε > 0, any simultaneous, randomized protocol that decides whether the welfare of the optimal partition is ≥ 1 or ≤ 3/4 – 1/108 + ε correctly with probability > 1/2 + 1/poly(m) requires exponential communication. This provides a separation between the attainable approximation guarantees via interactive (3/4) versus simultaneous (≤ 3/4 – 1/108) protocols with polynomial communication. In other words, this trivial reduction from decision to allocation problems provably requires the extra round of communication. We further discuss the implications of our results for the design of truthful combinatorial auctions in general, and extensions to general XOS valuations. In particular, our protocol for the allocation problem implies a new style of truthful mechanisms.

We study the active learning problem of top-k ranking from multi-wise comparisons under the popular multinomial logit model. Our goal is to identify the top-k items with high probability by adaptively querying sets for comparisons and observing the noisy output of the most preferred item from each comparison. To achieve this goal, we design a new active ranking algorithm without using any information about the underlying items’ preference scores. We also establish a matching lower bound on the sample complexity even when the set of preference scores is given to the algorithm. These two results together show that the proposed algorithm is nearly instance optimal (similar to instance optimal [12], but up to polylog factors). Our work extends the existing literature on rank aggregation in three directions. First, instead of studying a static problem with fixed data, we investigate the top-k ranking problem in an active learning setting. Second, we show our algorithm is nearly instance optimal, which is a much stronger theoretical guarantee. Finally, we extend the pairwise comparison to the multi-wise comparison, which has not been fully explored in ranking literature.

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a choice model in which each consumer selects a utility-maximizing bundle subject to a private valuation function, and study the complexity of the resulting optimization problem. Our main result is an exact algorithm for k -additive valuations, under a model of vertical differentiation in which customers agree on the relative value of each pair of items but differ in their absolute willingness to pay. For valuations that are vertically differentiated but not necessarily k -additive, we show how to obtain constant approximations under a “well-priced” condition, where each product’s price is sufficiently high. We further show that even for a single customer with known valuation, any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even when the valuation is succinctly representable.

Motivated by applications in recommender systems, web search, social choice, and crowdsourcing, we consider the problem of identifying the set of top K items from noisy pairwise comparisons. In our setting, we are given r pairwise comparisons between each pair of n items, where each comparison has noise constrained by a very general noise model called the strong stochastic transitivity model. Our goal is to provide an optimal instance adaptive algorithm for the top-K ranking problem. In particular, we present a linear time algorithm that has a competitive ratio of Õ(√n)1; i.e., to solve any instance of top-K ranking, our algorithm needs at most Õ(√n) times as many samples needed as the best possible algorithm for that instance [in contrast, all previous known algorithms for the topK problem have competitive ratios of Ω̃(n) or worse]. We further show that this is tight (up to polylogarithmic factors): any algorithm for the top-K problem has competitive ratio of at least Ω̃(√n).

Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top K items from noisy pairwise comparisons. In our setting, we are non-actively given r pairwise comparisons between each pair of n items, where each comparison has noise constrained by a very general noise model called the strong stochastic transitivity (SST) model. We analyze the competitive ratio of algorithms for the top-K problem. In particular, we present a linear time algorithm for the top-K problem which has a competitive ratio of i.e. to solve any instance of top-K, our algorithm needs at most times as many samples needed as the best possible algorithm for that instance (in contrast, all previous known algorithms for the top-K problem have competitive ratios of Ω(n) or worse). We further show that this is tight: any algorithm for the top-K problem has competitive ratio at least

We consider the question of interactive communication, in which two remote parties perform a computation, while their communication channel is (adversarially) noisy. We extend here the discussion into a more general and stronger class of noise, namely, we allow the channel to perform insertions and deletions of symbols. These types of errors may bring the parties “out of sync,” so that there is no consensus regarding the current round of the protocol. In this more general noise model, we obtain the first interactive coding scheme that has a constant rate and tolerates noise rates of up to 1/18 - ε. To this end, we develop a novel primitive we name edit-distance tree code. The edit-distance tree code is carefully designed to replace the Hamming distance constraints in Schulman's tree codes (IEEE Trans. Inf. Theory, 1996), with a stronger edit-distance requirement.

We study the communication complexity of combinatorial auctions via interpolation mechanisms that interpolate between non-truthful and truthful protocols. Specifically, an interpolation mechanism has two phases. In the first phase, the bidders participate in some non-truthful protocol whose output is itself a truthful protocol. In the second phase, the bidders participate in the truthful protocol selected during phase one. Note that virtually all existing auctions have either a non-existent first phase (and are therefore truthful mechanisms), or a non-existent second phase (and are therefore just traditional protocols, analyzed via the Price of Anarchy/Stability). The goal of this paper is to understand the benefits of interpolation mechanisms versus truthful mechanisms or traditional protocols, and develop the necessary tools to formally study them. Interestingly, we exhibit settings where interpolation mechanisms greatly outperform the optimal traditional and truthful protocols. Yet, we also exhibit settings where interpolation mechanisms are provably no better than truthful ones. Finally, we apply our new machinery to prove that the recent single-bid mechanism of Devanur et. al. [DMSW15] (the only pre-existing interpolation mechanism in the literature) achieves the optimal price of anarchy among a wide class of protocols, a claim that simply can't be addressed by appealing just to machinery from communication complexity or the study of truthful mechanisms.

We consider the problem of finding the kth highest element in a totally ordered set of n elements (Select), and partitioning a totally ordered set into the top k and bottom n − k elements (Partition) using pairwise comparisons. Motivated by settings like peer grading or crowdsourcing, where multiple rounds of interaction are costly and queried comparisons may be inconsistent with the ground truth, we evaluate algorithms based both on their total runtime and the number of interactive rounds in three comparison models: noiseless (where the comparisons are correct), erasure (where comparisons are erased with probability 1 − γ), and noisy (where comparisons are correct with probability 1/2 + γ/2 and incorrect otherwise). We provide numerous matching upper and lower bounds in all three models. Even our results in the noiseless model, which is quite well-studied in the TCS literature on parallel algorithms, are novel.

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with r rounds, we prove a lower bound of Omega(n/r) on the communication required for computing disjointness of input size n, which is optimal up to logarithmic factors. The previous best lower bound was Omega(n/r̂2) due to Jain, Radhakrishnan and Sen. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function f is at most 2 ̂O(QIC(f)), where QIC(f) is the prior-free quantum information complexity of f (with error 1/3).

We show that T rounds of interaction over the binary symmetric channel BSC1/2--ε with feedback can be simulated with O(ε2 T) rounds of interaction over a noiseless channel. We also introduce a more general "energy cost" model of interaction over a noisy channel. We show energy cost to be equivalent to external information complexity, which implies that our simulation results are unlikely to carry over to energy complexity. Our main technical innovation is a self-reduction from simulating a noisy channel to simulating a slightly-less-noisy channel, which may have other applications in the area of interactive compression.