Gagan Aggarwal

Gagan Aggarwal, Ashwinkumar Badanidiyuru, Paul Dütting et al.

Motivated by online retail, we consider the problem of selling one item (e.g., an ad slot) to two non-excludable buyers (say, a merchant and a brand). This problem captures, for example, situations where a merchant and a brand cooperatively bid in an auction to advertise a product, and both benefit from the ad being shown. A mechanism collects bids from the two and decides whether to allocate and which payments the two parties should make. This gives rise to intricate incentive compatibility constraints, e.g., on how to split payments between the two parties. We approach the problem of finding a revenue-maximizing incentive-compatible mechanism from an online learning perspective; this poses significant technical challenges. First, the action space (the class of all possible mechanisms) is huge; second, the function that maps mechanisms to revenue is highly irregular, ruling out standard discretization-based approaches. In the stochastic setting, we design an efficient learning algorithm achieving a regret bound of $O(T^{3/4})$. Our approach is based on an adaptive discretization scheme of the space of mechanisms, as any non-adaptive discretization fails to achieve sublinear regret. In the adversarial setting, we exploit the non-Lipschitzness of the problem to prove a strong negative result, namely that no learning algorithm can achieve more than half of the revenue of the best fixed mechanism in hindsight. We then consider the $σ$-smooth adversary; we construct an efficient learning algorithm that achieves a regret bound of $O(T^{2/3})$ and builds on a succinct encoding of exponentially many experts. Finally, we prove that no learning algorithm can achieve less than $Ω(\sqrt T)$ regret in both the stochastic and the smooth setting, thus narrowing the range where the minimax regret rates for these two problems lie.

Gagan Aggarwal, Anupam Gupta, Yifan Wang et al.

The "Trading Prophet" problem challenges an online trader to maximize its profit by buying and selling assets under stochastic prices and capacity constraints, competing against an offline prophet with full foresight. In previous work, each arriving asset was assumed to have a single price $p_t$, and the trader was allowed to either buy a copy at this price (subject to having available capacity), or sell a copy (if it already held at least one copy in hand). However, this abstraction can fail to capture the structural asymmetry of decentralized dealer-based markets, where buying and selling opportunities could be distinct, and driven by individual preferences. To address this, we introduce the Asymmetric Trading Prophets problem, where at each timestep the trader observes a price tuple $(b_t, s_t)$ -- representing the cost to buy, and the revenue from selling at this timestep. Importantly, the $(b_t,s_t)$ tuple could be potentially arbitrarily correlated. We provide the first competitive analysis for this asymmetric trading prophets problem, characterizing the achievable profit based on the trader's capacity $B$ and initial inventory $B_0$. For the unit-capacity case of $B=1$, we design online algorithms that achieve constant competitive ratios for both i.i.d. and non-i.i.d. distributions on the price tuples, when the trader has one initial copy ($B_0=1$). For the general capacity case where $B$ can be large, we give algorithms for i.i.d. distributions that achieve a competitive ratio of $1 - Θ(\log B_0/\sqrt{B_0})$. Finally, for the symmetric case (where the price tuple satisfies $b_t=s_t$), we improve this to get a competitive ratio of $1 - O(\log B/\sqrt{B})$, demonstrating that the performance approaches optimality as the capacity increases. We show that both ratios are tight up to a logarithmic factor.

Gagan Aggarwal, Giannis Fikioris, Mingfei Zhao

Advertisers increasingly use automated bidding to optimize their ad campaigns on online advertising platforms. Autobidding optimizes an advertiser's objective subject to various constraints, e.g. average ROI and budget constraints. In this paper, we study the problem of designing online autobidding algorithms to optimize value subject to ROI and budget constraints when the platform is running any mixture of first and second price auction. We consider the following stochastic setting: There is an item for sale in each of $T$ rounds. In each round, buyers submit bids and an auction is run to sell the item. We focus on one buyer, possibly with budget and ROI constraints. We assume that the buyer's value and the highest competing bid are drawn i.i.d. from some unknown (joint) distribution in each round. We design a low-regret bidding algorithm that satisfies the buyer's constraints. Our benchmark is the objective value achievable by the best possible Lipschitz function that maps values to bids, which is rich enough to best respond to many different correlation structures between value and highest competing bid. Our main result is an algorithm with full information feedback that guarantees a near-optimal $\tilde O(\sqrt T)$ regret with respect to the best Lipschitz function. Our result applies to a wide range of auctions, most notably any mixture of first and second price auctions (price is a convex combination of the first and second price). In addition, our result holds for both value-maximizing buyers and quasi-linear utility-maximizing buyers. We also study the bandit setting, where we show an $Ω(T^{2/3})$ lower bound on the regret for first-price auctions, showing a large disparity between the full information and bandit settings. We also design an algorithm with $\tilde O(T^{3/4})$ regret, when the value distribution is known and is independent of the highest competing bid.

Gagan Aggarwal, Anupam Gupta, Andres Perlroth et al.

We study a setting where agents use no-regret learning algorithms to participate in repeated auctions. \citet{kolumbus2022auctions} 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 for \emph{general deterministic} truthful auctions. We also show that the ratio of the learning rates of the bidders can \emph{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, \citet{myerson1981optimal} showed that revenue can be maximized by using a second-price auction with reserves.We show that, in stark contrast, in our setting with learning bidders, \emph{randomized} auctions can have strictly better revenue guarantees than second-price auctions with reserves, when $T$ is large enough. Finally, we study revenue maximization in the non-asymptotic regime. We define a notion of {\em auctioneer regret} comparing the revenue generated to the revenue of a second price auction with truthful bids. When the auctioneer has to use the same auction throughout the interaction, we show an (almost) tight regret bound of $\smash{\widetilde Θ(T^{3/4})}.$ If the auctioneer can change auctions during the interaction, but in a way that is oblivious to the bids, we show an (almost) tight bound of $\smash{\widetilde Θ(\sqrt{T})}.$

Laura Rebollo-Neira, Gagan Aggarwal

A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set called a dictionary. The proposed algorithm is tailored to be applied with trigonometric dictionaries. Its distinctive feature being that it avoids the need for the actual construction of the whole dictionary, by implementing the required operations via the Fast Fourier Transform. The achieved sparsity is theoretically equivalent to that rendered by the Orthogonal Matching Pursuit method. The contribution of the proposed dedicated implementation is to extend the applicability of the standard Orthogonal Matching Pursuit algorithm, by reducing its storage and computational demands. The suitability of the approach for producing sparse spectral models is illustrated by comparison with the traditional method, in the line of the Short Time Fourier Transform, involving only the corresponding orthonormal trigonometric basis.