arXiv subjects

Paul Dütting

Publications and source records attributed to Paul Dütting.

At least 19 recordsLinked to original sources

arXiv2026

Online Multi-Agent Contracts

We introduce and study an online variant of the multi-agent contract model. In our model, agents arrive one-by-one and are active with a certain probability. Upon arrival of agent $i$, the principal offers a linear contract $α_i$, specifying the fraction of the principal's reward transferred to agent $i$. Agents can either exert effort or not, incurring a cost if they do. The set of agents that exert effort determines the principal's expected reward through a reward function $f$. After all agents have arrived, the agents form a (pure) Nash equilibrium. As our main result we design an $O(1)$-competitive policy for submodular rewards, compared to the offline optimum. We also show that this result is tight in two ways. First, if we require that agents make decisions on the spot, then for submodular rewards any policy is $Ω((\log n)/(\log \log n)^2)$-competitive. Second, for the broader class of XOS (a.k.a., fractionally subadditive) rewards, any online policy is $Ω((\log \log n)/(\log \log \log n))$-competitive. The latter result reveals a surprising separation between submodular and XOS rewards: unlike related settings such as offline contract design and prophet inequalities, where constant-factor guarantees for submodular rewards extend to XOS rewards, the online contract setting separates the two classes.

cs.GT↗

arXiv2026

Graphic Matroid Secretary without the Graph

The matroid secretary problem (MSP) is one of the cleanest, and most captivating open problems in online algorithms. The famous MSP conjecture stipulates that there exists a constant-competitive algorithm, yet to date the best known algorithms are $O(\log \log (\text{rank}))$ competitive. It is widely believed that all information that an algorithm for the MSP should use is information that is available through an independence oracle on the already arrived elements. Despite this, there are natural classes of matroids where a constant-competitive algorithm is known if we are given additional upfront information about the matroid; while no such algorithm is known if all the algorithm can use is an independence oracle on the arrived elements. In this work, we tackle the perhaps most appealing such class of matroids, graphic matroids. We develop an algorithm for the MSP that has access to the independence oracle only. Our algorithm runs in polynomial time, and if the underlying matroid is graphic, it produces an independent set whose weight is at least $1/36$ of the maximum-weight independent set. Ours is the first constant-competitive algorithm for MSP on unknown graphic matroids.

cs.DS↗

arXiv2026

A General Framework for Dynamic Consistent Submodular Maximization

Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.

cs.DS↗

arXiv2026

Profit Maximization in Bilateral Trade against a Smooth Adversary

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, who wish to trade a good. We study this problem from the perspective of a profit-maximizing broker within an online learning framework, where the agents' valuations are generated by a smooth adversary. We devise a learning algorithm that guarantees a $\tilde{O}(\sqrt{T})$ regret bound, which is tight in the time horizon $T$ up to poly-logarithmic factors. This matches the minimax rate for the stochastic i.i.d. case, and is also well separated from the adversarial setting, where sublinear-regret is unattainable. By extending the strong regret guarantees from the i.i.d. case to the smooth adversary, we significantly broaden the scope of settings where such fast rate is achievable, while closing an important gap in the regret landscape of this fundamental economic problem. To overcome the challenges posed by this adversary, we leverage a continuity property of smooth instances and combines this with a hierarchical net-construction of the broker's action space, which is analyzed via algorithmic chaining. We showcase the applicability of these techniques by deriving a similarly tight $\tilde{O}(\sqrt{T})$ regret bound for a related mechanism design model: the joint ads problem.

cs.GT↗

arXiv2026

Autobidding Equilibria in Sponsored Shopping

As commerce shifts to digital marketplaces, platforms increasingly monetize traffic through Sponsored Shopping auctions. Unlike classic ``Sponsored Search", where an advertiser typically bids for a single link, these settings involve advertisers with broad catalogs of distinct products. In these auctions, a single advertiser can secure multiple slots simultaneously to promote different items within the same query. This creates a fundamental complexity: the allocation is combinatorial, as advertisers simultaneously win a bundle of slots rather than a single position. We study this setting through the lens of autobidding, where value-maximizing agents employ uniform bidding strategies to optimize total value subject to Return-on-Investment (ROI) constraints. We analyze two prevalent auction formats: Generalized Second-Price (GSP) and Vickrey-Clarke-Groves (VCG). Our first main contribution is establishing the universal existence of an Autobidding Equilibrium for both settings. Second, we prove a tight Price of Anarchy (PoA) of 2 for both mechanisms.

cs.GT↗

arXiv2025

Data-Driven Mechanism Design: Jointly Eliciting Preferences and Information

We study mechanism design in environments where agents have private preferences and private information about a common payoff-relevant state. In such settings with multi-dimensional types, standard mechanisms fail to implement efficient allocations. We address this limitation by proposing data-driven mechanisms that condition transfers on additional post-allocation information, modeled as an estimator of the payoff-relevant state. Our mechanisms extend the classic Vickrey-Clarke-Groves framework. We show they achieve exact implementation in posterior equilibrium when the state is fully revealed or utilities are affine in an unbiased estimator. With a consistent estimator, they achieve approximate implementation that converges to exact implementation as the estimator converges, and we provide bounds on the convergence rate. We demonstrate applications to digital advertising auctions and AI shopping assistants, where user engagement naturally reveals relevant information, and to procurement auctions with consumer spot markets, where additional information arises from a pricing game played by the same agents.

econ.TH↗

arXiv2025

When Contracts Get Complex: Information-Theoretic Barriers

In the combinatorial-action contract model (Dütting et al., FOCS'21) a principal delegates the execution of a complex project to an agent, who can choose any subset from a given set of actions. Each set of actions incurs a cost to the agent, given by a set function $c$, and induces an expected reward to the principal, given by a set function $f$. To incentivize the agent, the principal designs a contract that specifies the payment upon success, with the optimal contract being the one that maximizes the principal's utility. It is known that with access to value queries no constant-approximation is possible for submodular $f$ and additive $c$. A fundamental open problem is: does the problem become tractable with demand queries? We answer this question to the negative, by establishing that finding an optimal contract for submodular $f$ and additive $c$ requires exponentially many demand queries. We leverage the robustness of our techniques to extend and strengthen this result to different combinations of submodular/supermodular $f$ and $c$; while allowing the principal to access $f$ and $c$ using arbitrary communication protocols. Our results are driven by novel equal-revenue constructions when one of the functions is additive, immediately implying value query hardness. We then identify a new property -- sparse demand -- which allows us to strengthen these results to demand query hardness. Finally, by augmenting a perturbed version of these constructions with one additional action, thereby making both functions combinatorial, we establish exponential communication complexity.

cs.GT↗

arXiv2025

Black-Box Lifting and Robustness Theorems for Multi-Agent Contracts

Multi-agent contract design has largely evaluated contracts through the lens of pure Nash equilibria (PNE). This focus, however, is not without loss: In general, the principal can strictly gain by recommending a complex, possibly correlated, distribution over actions, while preserving incentive compatibility. In this work, we extend the analysis of multi-agent contracts beyond pure Nash equilibria to encompass more general equilibrium notions, including mixed Nash equilibria as well as (coarse-)correlated equilibria (CCE). The latter, in particular, captures the limiting outcome of agents engaged in learning dynamics. Our main result shows that for submodular and, more generally, XOS rewards, such complex recommendations yield at most a constant-factor gain: there exists a contract and a PNE whose utility is within a constant factor of the best CCE achievable by any contract. This provides a black-box lifting: results established against the best PNE automatically apply with respect to the best CCE, with only a constant factor loss. For submodular rewards, we further show how to transform a contract and a PNE of that contract into a new contract such that any of its CCEs gives a constant approximation to the PNE. This yields black-box robustness: up to constant factors, guarantees established for a specific contract and PNE automatically extend to the modified contract and any of its CCEs. We thus expand prior guarantees for multi-agent contracts and lower the barrier to new ones. As an important corollary, we obtain poly-time algorithms for submodular rewards that achieve constant approximations in any CCE, against the best CCE under the best contract. Such worst-case guarantees are provably unattainable for XOS rewards. Finally, we bound the gap between different equilibrium notions for subadditive, supermodular, and general rewards.

cs.GT↗

arXiv2025

Online Matroid Embeddings

We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. We establish the existence of such an embedding for binary matroids, and use it to relate variants of the binary matroid secretary problem to each other, showing that seemingly simpler problems are in fact equivalent to seemingly harder ones (up to constant-factors). Specifically, we show this to be the case for the version of the matroid secretary problem in which the matroid is not known in advance, and where it is known in advance. We also show that the version with known matroid structure, is equivalent to the problem where weights are not fully adversarial but drawn from a known pairwise-independent distribution.

cs.DS↗

arXiv2025

Nearly Tight Regret Bounds for Profit Maximization in Bilateral Trade

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. We study this problem from the perspective of a broker, in a regret minimization framework. At each time step, a new seller and buyer arrive, and the broker has to propose a mechanism that is incentive-compatible and individually rational, with the goal of maximizing profit. We propose a learning algorithm that guarantees a nearly tight $\tilde{O}(\sqrt{T})$ regret in the stochastic setting when seller and buyer valuations are drawn i.i.d. from a fixed and possibly correlated unknown distribution. We further show that it is impossible to achieve sublinear regret in the non-stationary scenario where valuations are generated upfront by an adversary. Our ambitious benchmark for these results is the best incentive-compatible and individually rational mechanism. This separates us from previous works on efficiency maximization in bilateral trade, where the benchmark is a single number: the best fixed price in hindsight. A particular challenge we face is that uniform convergence for all mechanisms' profits is impossible. We overcome this difficulty via a careful chaining analysis that proves convergence for a provably near-optimal mechanism at (essentially) optimal rate. We further showcase the broader applicability of our techniques by providing nearly optimal results for the joint ads problem.

cs.GT↗

arXiv2025

Approximate Optimality of Linear Contracts Under Uncertainty

We consider a hidden-action principal-agent model, in which actions require different amounts of effort, and the agent privately knows his ability that determines his cost of effort. We show that linear contracts admit approximation guarantees that improve with a natural metric that captures the degree of uncertainty in the contracting setting. We thus show that linear contracts are near-optimal whenever there is enough uncertainty. In contrast, other simple contract formats such as debt contracts may suffer from a loss linear in the number of possible actions, even when there is sufficient uncertainty.

cs.GT↗

arXiv2024

The Cost of Consistency: Submodular Maximization with Constant Recourse

In this work, we study online submodular maximization, and how the requirement of maintaining a stable solution impacts the approximation. In particular, we seek bounds on the best-possible approximation ratio that is attainable when the algorithm is allowed to make at most a constant number of updates per step. We show a tight information-theoretic bound of $\tfrac{2}{3}$ for general monotone submodular functions, and an improved (also tight) bound of $\tfrac{3}{4}$ for coverage functions. Since both these bounds are attained by non poly-time algorithms, we also give a poly-time randomized algorithm that achieves a $0.51$-approximation. Combined with an information-theoretic hardness of $\tfrac{1}{2}$ for deterministic algorithms from prior work, our work thus shows a separation between deterministic and randomized algorithms, both information theoretically and for poly-time algorithms.

cs.DS↗

arXiv2024

Principal-Agent Reinforcement Learning: Orchestrating AI Agents with Contracts

The increasing deployment of AI is shaping the future landscape of the internet, which is set to become an integrated ecosystem of AI agents. Orchestrating the interaction among AI agents necessitates decentralized, self-sustaining mechanisms that harmonize the tension between individual interests and social welfare. In this paper we tackle this challenge by synergizing reinforcement learning with principal-agent theory from economics. Taken separately, the former allows unrealistic freedom of intervention, while the latter struggles to scale in sequential settings. Combining them achieves the best of both worlds. We propose a framework where a principal guides an agent in a Markov Decision Process (MDP) using a series of contracts, which specify payments by the principal based on observable outcomes of the agent's actions. We present and analyze a meta-algorithm that iteratively optimizes the policies of the principal and agent, showing its equivalence to a contraction operator on the principal's Q-function, and its convergence to subgame-perfect equilibrium. We then scale our algorithm with deep Q-learning and analyze its convergence in the presence of approximation error, both theoretically and through experiments with randomly generated binary game-trees. Extending our framework to multiple agents, we apply our methodology to the combinatorial Coin Game. Addressing this multi-agent sequential social dilemma is a promising first step toward scaling our approach to more complex, real-world instances.

cs.GT↗

arXiv2024

Online Combinatorial Allocations and Auctions with Few Samples

In online combinatorial allocations/auctions, n bidders sequentially arrive, each with a combinatorial valuation (such as submodular/XOS) over subsets of m indivisible items. The aim is to immediately allocate a subset of the remaining items to maximize the total welfare, defined as the sum of bidder valuations. A long line of work has studied this problem when the bidder valuations come from known independent distributions. In particular, for submodular/XOS valuations, we know 2-competitive algorithms/mechanisms that set a fixed price for each item and the arriving bidders take their favorite subset of the remaining items given these prices. However, these algorithms traditionally presume the availability of the underlying distributions as part of the input to the algorithm. Contrary to this assumption, practical scenarios often require the learning of distributions, a task complicated by limited sample availability. This paper investigates the feasibility of achieving O(1)-competitive algorithms under the realistic constraint of having access to only a limited number of samples from the underlying bidder distributions. Our first main contribution shows that a mere single sample from each bidder distribution is sufficient to yield an O(1)-competitive algorithm for submodular/XOS valuations. This result leverages a novel extension of the secretary-style analysis, employing the sample to have the algorithm compete against itself. Although online, this first approach does not provide an online truthful mechanism. Our second main contribution shows that a polynomial number of samples suffices to yield a $(2+ε)$-competitive online truthful mechanism for submodular/XOS valuations and any constant $ε>0$. This result is based on a generalization of the median-based algorithm for the single-item prophet inequality problem to combinatorial settings with multiple items.

cs.GT↗

arXiv2024

Ambiguous Contracts

We explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity-averse and hence chooses an action that maximizes their minimum utility, the principal can strictly gain from using an ambiguous contract, and this gain can be arbitrarily high. We characterize the structure of optimal ambiguous contracts, showing that ambiguity drives optimal contracts towards simplicity. We also provide a characterization of ambiguity-proof classes of contracts, where the principal cannot gain by infusing ambiguity. Finally, we show that when the agent can engage in mixed actions, the advantages of ambiguous contracts disappear.

cs.GT↗

arXiv2024

Selling Joint Ads: A Regret Minimization Perspective

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.

cs.GT↗

arXiv2024

Consistent Submodular Maximization

Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with consistency constraints: elements arrive in a streaming fashion and the goal is maintaining a constant approximation to the optimal solution while having a stable solution (i.e., the number of changes between two consecutive solutions is bounded). We provide algorithms in this setting with different trade-offs between consistency and approximation quality. We also complement our theoretical results with an experimental analysis showing the effectiveness of our algorithms in real-world instances.

cs.DS↗

arXiv2024

Single-Sample Prophet Inequalities via Greedy-Ordered Selection

We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy, reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al.

cs.DS↗