online advertising platforms

Abstract: Automated mechanism design has enabled the learning of complex auction mechanisms using neural networks. However, designing non-truthful auctions remains challenging because bidders' equilibrium strategies depend on the auction mechanism and thus evolve as the mechanism is optimized. In this work, we formulate auction design as a Stackelberg game with multiple strategic followers and develop a fully first-order algorithm for revenue optimization in non-truthful auctions. We establish non-asymptotic guarantees for hypergradient approximation and show that, under standard smoothness and strong-monotonicity assumptions, our method reaches an $O(ε)$-stationary point using $\tilde{\mathcal{O}}(ε^{-2})$ first-order oracle calls. Experiments on symmetric and asymmetric single-item auctions, as well as multi-item auctions, show that our method converges faster than second- and zeroth-order baselines and scales better as the number of bidders increases. Our method also discovers auctions that achieve revenue close to truthful baselines. These results provide a scalable framework for automated mechanism design beyond truthful auctions.

Abstract: Online resource allocation faces two coupled challenges: (1) allocating scarce resources efficiently under uncertain future demand, and (2) ensuring that agents report task valuations and requirements truthfully (strategyproofness). Reinforcement Learning (RL) adapts allocation decisions through experience but does not necessarily ensure strategyproofness. Existing strategyproof RL uses a linear allocation rule, which limits the resource interactions it can represent. Neural mechanism design methods offer greater expressiveness, but provide only approximate incentive guarantees. Against this background, we introduce the first strategyproof deep RL mechanism for online resource allocation. It integrates three novel components: (i) a monotonic neural network that learns nonlinear interactions by construction (higher reported value cannot reduce acceptance, while a longer reported duration or larger resource requirement cannot increase it); (ii) a generalised critical payment: the lowest accepted value, with all other inputs fixed; and (iii) training by either RL or imitation of an existing rule. Together, monotonicity and the critical payment ensure strategyproofness and individual rationality, while the neural rule provides flexibility and imitation improves training efficiency. Empirically, on a four-resource stream with two partner pairs that a linear difference cannot represent, the neural rule achieves 97.8% of an offline welfare upper bound, compared with 93.8% for a linear learner and 89.0% for first-come, first-served, closing 65% and 80% of the remaining optimality gap, respectively. Moreover, imitation reaches 97.5% in only 261 seconds, about 89 times faster than RL.

Abstract: We study online fair division of indivisible goods among $n$ agents with frequency predictions: before any good arrives, the algorithm learns the multiset of each agent's values for the goods, but neither the arrival order nor which values of different agents belong to the same good. Neoh et al. (ICML 2026) showed that such predictions allow every share-based guarantee that is achievable offline, and left open whether a positive approximation of envy-freeness up to one good (EF1) is possible. We show that deterministic online algorithms can guarantee $1/2$-EF1 for three agents and $(3-\sqrt5)/2$-EF1 for four agents, whereas for five or more agents, no online algorithm can guarantee any positive approximation of EF1, even with $n+1$ goods and identical predictions. Together with the known result for two agents, a positive approximation of EF1 is therefore possible if and only if $n\leq4$. We also rule out any positive approximation of EFX for three or more agents, even when the valuations take only two distinct positive values. Next, we use the meta-algorithm of Neoh et al. (ICML 2026) to compute an epistemic EFX (EEFX) allocation in polynomial time for any $n$, and hence a $1/(n-1)$-EF$(n-2)$ allocation for $n\geq3$, whereas algorithms that fix a picking sequence in advance can guarantee a positive approximation of EF$k$ if and only if $n\leq k+2$. Finally, for noisy predictions, we give algorithms that return EEFX allocations when the predictions are exact, and guarantee $(1-2\varepsilon+O(\varepsilon^2))$-EEFX under underestimates and, for $n\geq3$, $(1-2(n-1)\varepsilon+O(\varepsilon^2))$-EEFX under overestimates; the linear terms are the best possible, and larger overestimates rule out any positive approximation for such algorithms.

Abstract: As AI agents reshape Web search and advertising, platforms can monetize information that improves decisions. We study information pricing for sequential search among independent alternatives with nonobligatory inspection: the buyer may select any alternative without buying its report. We show that a common fee maximizes static revenue for identical priors, resolving a uniform-pricing conjecture. Our results also establish that exact optimization is NP-hard for heterogeneous binary priors. Despite this hardness, our polynomial-time static pricing algorithm achieves a $3$-approximation to the information surplus. More generally, a common static fee approximates optimal adaptive revenue within a logarithmic factor in the number of alternatives. This guarantee is asymptotically tight.

Abstract: Position auctions require assigning advertisers to positions and determining their display order. Under cascade behavior, earlier clicks prevent users from reaching later placements, coupling the click probabilities of selected advertisements. Existing methods achieve constant-factor welfare approximation and monotone logarithmic-factor approximation separately, leaving open whether both guarantees can be attained simultaneously. The difficulty is that welfare-preserving rounding need not maintain the monotonicity of individual click-through rates required for truthful bidding. We resolve this problem by developing a polynomial-time randomized mechanism that achieves a factor-6 welfare approximation and truthfulness in expectation for arbitrary public advertiser-position click probabilities. The mechanism optimizes a reach-weighted linear relaxation and converts its solution into feasible ordered allocations through matching decomposition, probability-bounded grouping, and calibrated attenuation. This construction compensates for cascade dependence and ensures that each advertiser's expected click-through rate equals exactly one sixth of its fractional click coordinate. The resulting identity transfers the monotonicity of the fractional allocation to the implemented mechanism, enabling exact incentive-compatible payments while preserving the welfare guarantee. The allocation lottery and payments are computable in polynomial bit time, with exact sampling in expected polynomial time.

Abstract: Autobidding has become a dominant paradigm in online advertising by enabling advertisers to set high-level goals while algorithms handle real-time bid optimization. A prominent example is the Return-on-Spend (RoS) value maximizer, which maximizes total value subject to an aggregate value-per-spend constraint. While most work on mechanism design for autobidders focuses on one-sided markets, many real-world platforms involve strategic behavior on both sides. We initiate the study of two-sided markets with autobidders. We first establish a stark negative result: for the challenging objective of liquid gains from trade (LGFT) in the prior-free setting, broad classes of utility-truthful, budget-balanced mechanisms have unbounded Price of Anarchy (PoA) once value-maximizing agents are present, even in double-auction environments. We then give two positive results. In the prior-free repeated double-auction setting, McAfee's Trade Reduction mechanism has unbounded PoA for LGFT but achieves constant PoA for liquid welfare under RoS bidding, showing that off-the-shelf mechanisms retain meaningful welfare guarantees. With distributional information regarding the private costs and values, we design a two-sided mechanism that is incentive compatible for each agent under its corresponding objective, individually rational, ex-ante weakly budget balanced, and achieves first-best liquid welfare, equivalently optimal LGFT, whenever at least one side of the market consists of RoS value maximizers. This result applies to matching markets with general downward-closed feasibility constraints. It contrasts sharply with the Myerson--Satterthwaite impossibility theorem~\citep{MS83}, which rules out first-best efficiency with incentive compatibility, individual rationality, and budget balance even in bilateral trade when both the buyer and the seller are quasi-linear utility maximizers.

Abstract: Auto-bidding is now widely adopted in online advertising platforms, allowing advertisers to specify high-level campaign objectives--such as maximizing total value subject to a return-on-spend (ROS) constraint--rather than manual per-query bids. A central question in algorithmic mechanism design is characterizing the worst-case efficiency loss, or Price of Anarchy (PoA), across auction formats in this prior-free setting. While randomized auctions are known to strictly improve efficiency over deterministic mechanisms for two bidders, two fundamental questions have remained open: (1) what is the optimal PoA for two bidders, and (2) can any mechanism beat the barrier of 2 for general $n \ge 3$ bidders? We resolve both questions using the family of $r$-proportional first-price auctions ($\text{pFPA}_r$), in which each bidder wins with probability proportional to their bid raised to an exponent $r > 0$ and pays their bid upon winning. First, for two bidders, we prove that the standard proportional first-price auction ($r = 1$) achieves a tight $\text{PoA} \le 1.5$, complemented by a matching lower bound showing that no anonymous, monotone mechanism can do better. Second, for general $n \ge 2$ bidders, setting $r = 2n$ achieves $\text{PoA} \le 2 - \frac{1}{4n+1} = 2 - Ω(1/n)$ across all undominated bid profiles, breaking the deterministic barrier of 2 for every finite $n$ and asymptotically matching the known $2 - Θ(1/n)$ lower bound.

Abstract: The return-on-investment (ROI) constraint is central to many auctions, particularly in online advertising, where a bidder is unwilling to pay more than a fixed fraction of the value obtained. We study truthful and revenue-maximizing auctions for ROI-constrained bidders. We first characterize truthful auctions when both valuations and ROI constraints are private, showing that the allocation rule uniquely determines the payment rule. Building on this characterization, for multiple bidders we introduce $σ$-increment mechanisms that resemble Myerson's optimal mechanism~\cite{journals/mor/Myerson81}; as $σ$ vanishes, these mechanisms become asymptotically optimal among deterministic truthful mechanisms, and their revenue approaches at least a $1/\bar r$ fraction of the optimal expected revenue over all truthful mechanisms, where $\bar r$ is the largest possible ROI constraint. In the single-bidder setting, we prove that every truthful auction can be replaced by a convex pricing function with weakly higher payments for every type, and we derive the optimal pricing functions when either the valuation or the ROI constraint is public.

Abstract: Online fair division captures allocation problems in which indivisible resources arrive over time and must be assigned before future resources are known. Understanding what fairness remains achievable when allocation decisions are immediate and irrevocable is a fundamental question in this setting. We study deterministic online allocation among $n$ agents with nonnegative additive valuations, where the number of goods is unknown and the adversary can adapt to previous allocation decisions. We focus on proportionality up to one good (PROP1) and examine how advance future information affects the achievable guarantees. In the setting without additional information, we answer an open question in Choo et al. that asks whether a nontrivial deterministic approximation for PROP1 can be obtained. In particular, we present a deterministic algorithm that guarantees $Ω(1/\log(nm))$-PROP1, where $m$ is the number of goods. Moreover, we complement this result by showing that, for every fixed $n$ and all sufficiently large $m$, every deterministic algorithm has an instance with $m$ goods on which its PROP1 factor is $O(\log\log m/\log m)$. We also study the setting where the algorithm knows in advance the maximum item value (MIV) for every agent. With MIV information, we give a deterministic algorithm with competitive ratio 1/2, improving the $1/n$ guarantee in Choo et al. We also show that no deterministic algorithm can achieve a competitive ratio arbitrarily close to one, even for two agents with exact MIV information.

Abstract: We study switching regret in adversarial multi-armed bandits, where the learner competes with an arm sequence that changes at most $S$ times. When $S$ is known, an optimal expected regret of $\widetilde{\mathcal{O}}(\sqrt{(S+1)KT})$ is obtainable [Auer et al., 2002]. However, when $S$ is unknown, Marinov and Zimmert [2021] show that this guarantee is impossible under an adaptive adversary. In this paper, we show that a single algorithm achieves $\widetilde{\mathcal{O}}(\sqrt{(S+1)KT})$ expected regret for every $S$ against an oblivious adversary, resolving an open problem of Auer et al. [2019b]. Our algorithm combines a fixed-share learner initialized with a small learning rate and dyadic-interval subroutines that search for local improvements using randomized learning rates and implicit exploration. Importantly, a non-uniform prior favors following the main learner, keeping the cost of maintaining many subroutines small. When the subroutines accumulate sufficient improvement over the main learner, its learning rate doubles, allowing adaptation to the unknown number of comparator switches $S$.