We consider the problem of designing contextual bandit algorithms in the "cross-learning" setting of Balseiro et al., where the learner observes the loss for the action

We consider the problem of designing contextual bandit algorithms in the "cross-learning" setting of Balseiro et al., where the learner observes the loss for the action

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 $1$.

We study the problem of learning Bayesian-optimal revenue-maximizing auctions. The classical approach to maximizing revenue requires a known prior distribution on the demand of the bidders, although recent work has shown how to replace the knowledge of a prior distribution with a polynomial sample. However, in an online setting, when buyers can participate in multiple rounds, standard learning techniques are susceptible to \emph{strategic overfitting}: bidders can improve their long-term wellbeing by manipulating the trajectory of the learning algorithm in earlier rounds. For example, they may be able to strategically adjust their behavior in earlier rounds to achieve lower, more favorable future prices. Such non-truthful behavior can hinder learning and harm revenue. In this paper, we combine tools from differential privacy, mechanism design, and sample complexity to give a repeated auction that (1) learns bidder demand from past data, (2) is approximately revenue-optimal, and (3) strategically robust, as it incentivizes bidders to behave truthfully.

We consider the problem of learning optimal reserve price in repeated auctions against non-myopic bidders, who may bid strategically in order to gain in future rounds even if the single-round auctions are truthful. Previous algorithms, e.g., empirical pricing, do not provide non-trivial regret rounds in this setting in general. We introduce algorithms that obtain small regret against non-myopic bidders either when the market is large, i.e., no bidder appears in a constant fraction of the rounds, or when the bidders are impatient, i.e., they discount future utility by some factor mildly bounded away from one. Our approach carefully controls what information is revealed to each bidder, and builds on techniques from differentially private online learning as well as the recent line of works on jointly differentially private algorithms.

We study a setting where agents use no-regret learning algorithms to participate in repeated auctions. Recently, Kolumbus and Nisan [2022a] showed, rather surprisingly, that when bidders participate in second-price auctions using no-regret bidding algorithms, no matter how large the number of interactions $T$ is, the runner-up bidder may not converge to bidding truthfully. Our first result shows that this holds forall deterministictruthful auctions. We also show that the ratio of the learning rates of different bidders can qualitatively affect the convergence of the bidders. Next, we consider the problem of revenue maximization in this environment. In the setting with fully rational bidders, the seminal result of Myerson [1981] showed that revenue can be maximized by using a second-price auction with reserves.

We consider the problem of a revenue-maximizing seller with a large number of items $m$ for sale to $n$ strategic bidders, whose valuations are drawn independently from high-dimensional, unknown prior distributions. It is well-known that optimal and even approximately-optimal mechanisms for this setting are notoriously difficult to characterize or compute, and, even when they can be found, are often rife with various counter-intuitive properties. In this paper, following a model introduced recently by Cai and Daskalakis [CD22], we consider the case that bidders' prior distributions can be well-approximated by a topic model. We design an active learning component, responsible for interacting with the bidders and outputting low-dimensional approximations of their types, and a mechanism design component, responsible for robustifying mechanisms for the low-dimensional model to work for the approximate types of the former component. On the active learning front, we cast our problem in the framework of Randomized Linear Algebra (RLA) for regression problems, allowing us to import several breakthrough results from that line of research, and adapt them to our setting. On the mechanism design front, we remove many restrictive assumptions of prior work on the type of access needed to the underlying distributions and the associated mechanisms. To the best of our knowledge, our work is the first to formulate connections between mechanism design, and RLA for active learning of regression problems, opening the door for further applications of randomized linear algebra primitives to mechanism design.

We study the problem of learning revenue-optimal multi-bidder auctions from samples when the samples of bidders' valuations can be adversarially corrupted or drawn from distributions that are adversarially perturbed. First, we prove tight upper bounds on the revenue we can obtain with a corrupted distribution under a population model, for both regular valuation distributions and distributions with monotone hazard rate (MHR). We then propose new algorithms that, given only an ``approximate distribution'' for the bidder's valuation, can learn a mechanism whose revenue is nearly optimal simultaneously for all ``true distributions'' that are $\alpha$-close to the original distribution in Kolmogorov-Smirnov distance. The proposed algorithms operate beyond the setting of bounded distributions that have been studied in prior works, and are guaranteed to obtain a fraction $1-O(\alpha)$ of the optimal revenue under the true distribution when the distributions are MHR. Moreover, they are guaranteed to yield at least a fraction $1-O(\sqrt{\alpha})$ of the optimal revenue when the distributions are regular. We prove that these upper bounds cannot be further improved, by providing matching lower bounds. Lastly, we derive sample complexity upper bounds for learning a near-optimal auction for both MHR and regular distributions.