arXiv subjects

Michal Feldman

Publications and source records attributed to Michal Feldman.

At least 37 records · Page 2Linked to original sources

arXiv2025

Budget-Feasible Contracts

The problem of computing near-optimal contracts in combinatorial settings has recently attracted significant interest in the computer science community. Previous work has provided a rich body of structural and algorithmic insights into this problem. However, most of these results rely on the assumption that the principal has an unlimited budget for incentivizing agents, an assumption that is often unrealistic in practice. This motivates the study of the optimal contract problem under budget constraints. In this work, we study multi-agent contracts with binary actions under budget constraints. Our contribution is threefold. First, we show that all previously known approximation guarantees on the principal's utility extend (asymptotically) to budgeted settings. Second, through the lens of budget constraints, we uncover insightful connections between the standard objective of maximizing the principal's utility and other relevant objectives. Specifically, we identify a broad class of objectives, which we term BEST (BEyond STandard) objectives, including reward, social welfare, and principal's utility, and show that they are all equivalent (up to a constant factor), leading to approximation guarantees for all BEST objectives. Third, we introduce the price of frugality, which quantifies the loss due to budget constraints, and establish near-tight bounds on this measure, providing deeper insights into the tradeoffs between budgets and incentives.

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arXiv2025

Contract Design for Sequential Actions

We introduce a novel model of contracts with combinatorial actions that accounts for sequential and adaptive agent behavior. As in the standard model, a principal delegates the execution of a costly project to an agent. There are $n$ actions, each one incurring a cost to the agent and inducing a probability distribution over $m$ outcomes; each outcome generates some reward for the principal. The principal incentivizes the agent through a contract that specifies a payment for each potential outcome. Unlike the standard model, the agent chooses actions sequentially. Following each action, the agent observes the realized outcome, and decides whether to stop or continue with another action. Upon halting, the agent chooses one of the realized outcomes, which determines both his payment and the principal's reward. This model captures common scenarios where the agent can make multiple attempts in the course of executing a project. We study the optimal contract problem in this new setting, namely the contract that maximizes the principal's utility. We first observe that the agent's problem - (adaptively) finding the sequence of actions that maximizes his utility for a given contract - is equivalent to the well-known Pandora's Box problem. Using this insight, we provide algorithms and hardness results for the optimal contract problem, under both independent and correlated actions, and for both linear and general contracts. For independent actions, we provide a poly-time algorithm for the optimal linear contract, and establish that finding the optimal general contract is NP-hard. In cases where the number of outcomes is constant, we devise a poly-time algorithm even for the optimal general contract. For correlated actions, we find that, for both linear and general contracts, approximating the optimal contract within any constant ratio is NP-hard.

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arXiv2025

The Pseudo-Dimension of Contracts

Algorithmic contract design studies scenarios where a principal incentivizes an agent to exert effort on her behalf. In this work, we focus on settings where the agent's type is drawn from an unknown distribution, and formalize an offline learning framework for learning near-optimal contracts from sample agent types. A central tool in our analysis is the notion of pseudo-dimension from statistical learning theory. Beyond its role in establishing upper bounds on the sample complexity, pseudo-dimension measures the intrinsic complexity of a class of contracts, offering a new perspective on the tradeoffs between simplicity and optimality in contract design. Our main results provide essentially optimal tradeoffs between pseudo-dimension and representation error (defined as the loss in principal's utility) with respect to linear and bounded contracts. Using these tradeoffs, we derive sample- and time-efficient learning algorithms, and demonstrate their near-optimality by providing almost matching lower bounds on the sample complexity. Conversely, for unbounded contracts, we prove an impossibility result showing that no learning algorithm exists. Finally, we extend our techniques in three important ways. First, we provide refined pseudo-dimension and sample complexity guarantees for the combinatorial actions model, revealing a novel connection between the number of critical values and sample complexity. Second, we extend our results to menus of contracts, showing that their pseudo-dimension scales linearly with the menu size. Third, we adapt our algorithms to the online learning setting, where we show that, a polynomial number of type samples suffice to learn near-optimal bounded contracts. Combined with prior work, this establishes a formal separation between expert advice and bandit feedback for this setting.

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arXiv2024

Algorithmic Contract Theory: A Survey

A contract is an economic tool used by a principal to incentivize one or more agents to exert effort on her behalf, by defining payments based on observable performance measures. A key challenge addressed by contracts -- known in economics as moral hazard -- is that, absent a properly set up contract, agents might engage in actions that are not in the principal's best interest. Another common feature of contracts is limited liability, which means that payments can go only from the principal -- who has the deep pocket -- to the agents. With classic applications of contract theory moving online, growing in scale, and becoming more data-driven, tools from contract theory become increasingly important for incentive-aware algorithm design. At the same time, algorithm design offers a whole new toolbox for reasoning about contracts, ranging from additional tools for studying the tradeoff between simple and optimal contracts, through a language for discussing the computational complexity of contracts in combinatorial settings, to a formalism for analyzing data-driven contracts. This survey aims to provide a computer science-friendly introduction to the basic concepts of contract theory. We give an overview of the emerging field of "algorithmic contract theory" and highlight work that showcases the potential for interaction between the two areas. We also discuss avenues for future research.

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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.

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arXiv2024

Learning-Augmented Metric Distortion via $(p,q)$-Veto Core

In the metric distortion problem there is a set of candidates $C$ and voters $V$ in the same metric space. The goal is to select a candidate minimizing the social cost: the sum of distances of the selected candidate from all the voters, and the challenge arises from the algorithm receiving only ordinaL input: each voter's ranking of candidate, while the objective function is cardinal, determined by the underlying metric. The distortion of an algorithm is its worst-case approximation factor of the optimal social cost. A key concept here is the (p,q)-veto core, with $p\in Δ(V)$ and $q\in Δ(C)$ being normalized weight vectors representing voters' veto power and candidates' support, respectively. The (p,q)-veto core corresponds to a set of winners from a specific class of deterministic algorithms. Notably, the optimal distortion of $3$ is obtained from this class, by selecting veto core candidates using uniform $p$ and $q$ proportional to candidates' plurality scores. Bounding the distortion of other algorithms from this class is an open problem. Our contribution is twofold. First, we establish upper bounds on the distortion of candidates from the (p,q)-veto core for arbitrary weight vectors $p$ and $q$. Second, we revisit the metric distortion problem through the \emph{learning-augmented} framework, which equips the algorithm with a (machine-learned) prediction regarding the optimal candidate. The quality of this prediction is unknown, and the goal is to optimize the algorithm's performance under accurate predictions (consistency), while simultaneously providing worst-case guarantees under arbitrarily inaccurate predictions (robustness). We propose an algorithm that chooses candidates from the (p,q)-veto core, using a prediction-guided q vector and, leveraging our distortion bounds, we prove that this algorithm achieves the optimal robustness-consistency trade-off.

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arXiv2024

Multi-Agent Combinatorial Contracts

Combinatorial contracts are emerging as a key paradigm in algorithmic contract design, paralleling the role of combinatorial auctions in algorithmic mechanism design. In this paper we study natural combinatorial contract settings involving teams of agents, each capable of performing multiple actions. This scenario extends two fundamental special cases previously examined in the literature, namely the single-agent combinatorial action model of [Duetting et al., 2021] and the multi-agent binary-action model of [Babaioff et al., 2012, Duetting et al., 2023]. We study the algorithmic and computational aspects of these settings, highlighting the unique challenges posed by the absence of certain monotonicity properties essential for analyzing the previous special cases. To navigate these complexities, we introduce a broad set of novel tools that deepen our understanding of combinatorial contracts environments and yield good approximation guarantees. Our main result is a constant-factor approximation for submodular multi-agent multi-action problems with value and demand oracles access. This result is tight: we show that this problem admits no PTAS (even under binary actions). As a side product of our main result, we devise an FPTAS, with value and demand oracles, for single-agent combinatorial action scenarios with general reward functions, which is of independent interest. We also provide bounds on the gap between the optimal welfare and the principal's utility. We show that, for subadditive rewards, perhaps surprisingly, this gap scales only logarithmically (rather than linearly) in the size of the action space.

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arXiv2024

Choosing Behind the Veil: Tight Bounds for Identity-Blind Online Algorithms

In Bayesian online settings, every element has a value that is drawn from a known underlying distribution, which we refer to as the element's identity. The elements arrive sequentially. Upon the arrival of an element, its value is revealed, and the decision maker needs to decide, immediately and irrevocably, whether to accept it or not. While most previous work has assumed that the decision maker, upon observing the element's value, also becomes aware of its identity -- namely, its distribution -- practical scenarios frequently demand that decisions be made based solely on the element's value, without considering its identity. This necessity arises either from the algorithm's ignorance of the element's identity or due to the pursuit of fairness. We call such algorithms identity-blind algorithms, and propose the identity-blindness gap as a metric to evaluate the performance loss caused by identity-blindness. This gap is defined as the maximum ratio between the expected performance of an identity-blind online algorithm and an optimal online algorithm that knows the arrival order, thus also the identities. We study the identity-blindness gap in the paradigmatic prophet inequality problem, under the two objectives of maximizing the expected value, and maximizing the probability to obtain the highest value. For the max-expectation objective, the celebrated prophet inequality establishes a single-threshold algorithm that gives at least 1/2 of the offline optimum, thus also an identity-blindness gap of at least 1/2. We show that this bound is tight. For the max-probability objective, while the competitive ratio is tightly 1/e, we provide a deterministic single-threshold algorithm that gives an identity-blindness gap of $\sim 0.562$ under the assumption that there are no large point masses. Moreover, we show that this bound is tight with respect to deterministic algorithms.

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arXiv2024

The Competition Complexity of Prophet Inequalities

We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the $(1-\varepsilon)$-competition complexity of different types of online algorithms. This metric asks for the smallest $k$ such that the expected value of the online algorithm on $k$ copies of the original instance, is at least a $(1-\varepsilon)$-approximation to the expected offline optimum on a single copy. We show that block threshold algorithms, which set one threshold per copy, are optimal and give a tight bound of $k = Θ(\log \log 1/\varepsilon)$. This shows that block threshold algorithms approach the offline optimum doubly-exponentially fast. For single threshold algorithms, we give a tight bound of $k = Θ(\log 1/\varepsilon)$, establishing an exponential gap between block threshold algorithms and single threshold algorithms. Our model and results pave the way for exploring resource-augmented prophet inequalities in combinatorial settings. In line with this, we present preliminary findings for bipartite matching with one-sided vertex arrivals, as well as in XOS combinatorial auctions. Our results have a natural competition complexity interpretation in mechanism design and pricing applications.

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arXiv2024

Private Interdependent Valuations: New Bounds for Single-Item Auctions and Matroids

We study auction design within the widely acclaimed model of interdependent values, introduced by Milgrom and Weber [1982]. In this model, every bidder $i$ has a private signal $s_i$ for the item for sale, and a public valuation function $v_i(s_1,\ldots,s_n)$ which maps every vector of private signals (of all bidders) into a real value. A recent line of work established the existence of approximately-optimal mechanisms within this framework, even in the more challenging scenario where each bidder's valuation function $v_i$ is also private. This body of work has primarily focused on single-item auctions with two natural classes of valuations: those exhibiting submodularity over signals (SOS) and $d$-critical valuations. In this work we advance the state of the art on interdependent values with private valuation functions, with respect to both SOS and $d$-critical valuations. For SOS valuations, we devise a new mechanism that gives an improved approximation bound of $5$ for single-item auctions. This mechanism employs a novel variant of an "eating mechanism", leveraging LP-duality to achieve feasibility with reduced welfare loss. For $d$-critical valuations, we broaden the scope of existing results beyond single-item auctions, introducing a mechanism that gives a $(d+1)$-approximation for any environment with matroid feasibility constraints on the set of agents that can be simultaneously served. Notably, this approximation bound is tight, even with respect to single-item auctions.

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arXiv2024

On Optimal Tradeoffs between EFX and Nash Welfare

A major problem in fair division is how to allocate a set of indivisible resources among agents fairly and efficiently. The goal of this work is to characterize the tradeoffs between two well-studied measures of fairness and efficiency -- envy freeness up to any item (EFX) for fairness, and Nash welfare for efficiency -- by saying, for given constants $α$ and $β$, whether there exists an $α$-EFX allocation that guarantees a $β$-fraction of the maximum Nash welfare ($β$-MNW). For additive valuations, we show that for any $α\in [0,1]$, there exists a partial allocation that is $α$-EFX and $\frac{1}{α+1}$-MNW, and this tradeoff is tight (for any $α$). We also show that for $α\in[0,φ-1 \approx 0.618]$ these partial allocations can be turned into complete allocations where all items are assigned. Furthermore, for any $α\in [0, 1/2]$, we show that the tight tradeoff of $α$-EFX and $\frac{1}{α+1}$-MNW with complete allocations holds for the more general setting of subadditive valuations. Our results improve upon the current state of the art, for both additive and subadditive valuations, and match the best-known approximations of EFX under complete allocations, regardless of Nash welfare guarantees. Notably, our constructions for additive valuations also provide EF1 and constant approximations for maximin share guarantees.

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arXiv2023

Fair Division via Quantile Shares

We consider the problem of fair division, where a set of indivisible goods should be distributed fairly among a set of agents with combinatorial valuations. To capture fairness, we adopt the notion of shares, where each agent is entitled to a fair share, based on some fairness criterion, and an allocation is considered fair if the value of every agent (weakly) exceeds her fair share. A share-based notion is considered universally feasible if it admits a fair allocation for every profile of monotone valuations. A major question arises: is there a non-trivial share-based notion that is universally feasible? The most well-known share-based notions, namely proportionality and maximin share, are not universally feasible, nor are any constant approximations of them. We propose a novel share notion, where an agent assesses the fairness of a bundle by comparing it to her valuation in a random allocation. In this framework, a bundle is considered $q$-quantile fair, for $q\in[0,1]$, if it is at least as good as a bundle obtained in a uniformly random allocation with probability at least $q$. Our main question is whether there exists a constant value of $q$ for which the $q$-quantile share is universally feasible. Our main result establishes a strong connection between the feasibility of quantile shares and the classical Erdős Matching Conjecture. Specifically, we show that if a version of this conjecture is true, then the $\frac{1}{2e}$-quantile share is universally feasible. Furthermore, we provide unconditional feasibility results for additive, unit-demand and matroid-rank valuations for constant values of $q$. Finally, we discuss the implications of our results for other share notions.

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arXiv2023

On the (In)approximability of Combinatorial Contracts

We study two combinatorial contract design models -- multi-agent and multi-action -- where a principal delegates the execution of a costly project to others. In both settings, the principal cannot observe the choices of the agent(s), only the project's outcome (success or failure), and incentivizes the agent(s) using a contract, which is a payment scheme that specifies the payment to the agent(s) upon a project's success. In the multi-agent setting, the project is delegated to a team of agents, and every agent chooses whether or not to exert effort. A success probability function specifies the probability of success for every subset of agents exerting effort. For the family of submodular success probability functions, Duetting et al. [2023] established a poly-time constant-factor approximation to the optimal contract, and left open whether this problem admits a PTAS. We show that no poly-time algorithm guarantees a better than $0.7$-approximation to the optimal contract. For XOS functions, Duetting et al. [2023] give a poly-time constant approximation with value and demand queries. We show that with value queries only, one cannot get any constant approximation. In the multi-action setting, the project is delegated to a single agent, who can take any subset of a given set of actions. Here, a success probability function specifies the probability of success for any subset of actions. Duetting et al. [2021a] devised a poly-time algorithm for computing an optimal contract for gross substitutes success probability functions, and established NP-hardness with respect to submodular functions. We further strengthen this hardness result by showing that this problem does not admit any constant approximation either. For the broader class of XOS functions, we establish the hardness of obtaining a $n^{-1/2+\varepsilon}$-approximation for any $\varepsilon > 0$.

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arXiv2023

Constant Approximation for Private Interdependent Valuations

The celebrated model of auctions with interdependent valuations, introduced by Milgrom and Weber in 1982, has been studied almost exclusively under private signals $s_1, \ldots, s_n$ of the $n$ bidders and public valuation functions $v_i(s_1, \ldots, s_n)$. Recent work in TCS has shown that this setting admits a constant approximation to the optimal social welfare if the valuations satisfy a natural property called submodularity over signals (SOS). More recently, Eden et al. (2022) have extended the analysis of interdependent valuations to include settings with private signals and private valuations, and established $O(\log^2 n)$-approximation for SOS valuations. In this paper we show that this setting admits a constant factor approximation, settling the open question raised by Eden et al. (2022).

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arXiv2023

Combinatorial Contracts Beyond Gross Substitutes

We study the combinatorial contracting problem of Dütting et al. [FOCS '21], in which a principal seeks to incentivize an agent to take a set of costly actions. In their model, there is a binary outcome (the agent can succeed or fail), and the success probability and the costs depend on the set of actions taken. The optimal contract is linear, paying the agent an $α$ fraction of the reward. For gross substitutes (GS) rewards and additive costs, they give a poly-time algorithm for finding the optimal contract. They use the properties of GS functions to argue that there are poly-many "critical values" of $α$, and that one can iterate through all of them efficiently in order to find the optimal contract. In this work we study to which extent GS rewards and additive costs constitute a tractability frontier for combinatorial contracts. We present an algorithm that for any rewards and costs, enumerates all critical values, with poly-many demand queries (in the number of critical values). This implies the tractability of the optimal contract for any setting with poly-many critical values and efficient demand oracle. A direct corollary is a poly-time algorithm for the optimal contract in settings with supermodular rewards and submodular costs. We also study a natural class of matching-based instances with XOS rewards and additive costs. While the demand problem for this setting is tractable, we show that it admits an exponential number of critical values. On the positive side, we present (pseudo-) polynomial-time algorithms for two natural special cases of this setting. Our work unveils a profound connection to sensitivity analysis, and designates matching-based instances as a crucial focal point for gaining a deeper understanding of combinatorial contract settings.

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arXiv2023

Breaking the Envy Cycle: Best-of-Both-Worlds Guarantees for Subadditive Valuations

We study best-of-both-worlds guarantees for the fair division of indivisible items among agents with subadditive valuations. Our main result establishes the existence of a random allocation that is simultaneously ex-ante $\frac{1}{2}$-envy-free, ex-post $\frac{1}{2}$-EFX and ex-post EF1, for every instance with subadditive valuations. We achieve this result by a novel polynomial-time algorithm that randomizes the well-established envy cycles procedure in a way that provides ex-ante fairness. Notably, this is the first best-of-both-worlds fairness guarantee for subadditive valuations, even when considering only EF1 without EFX.

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arXiv2023

Pandora's Problem with Combinatorial Cost

Pandora's problem is a fundamental model in economics that studies optimal search strategies under costly inspection. In this paper we initiate the study of Pandora's problem with combinatorial costs, capturing many real-life scenarios where search cost is non-additive. Weitzman's celebrated algorithm [1979] establishes the remarkable result that, for additive costs, the optimal search strategy is non-adaptive and computationally feasible. We inquire to which extent this structural and computational simplicity extends beyond additive cost functions. Our main result is that the class of submodular cost functions admits an optimal strategy that follows a fixed, non-adaptive order, thus preserving the structural simplicity of additive cost functions. In contrast, for the more general class of subadditive (or even XOS) cost functions, the optimal strategy may already need to determine the search order adaptively. On the computational side, obtaining any approximation to the optimal utility requires super polynomially many queries to the cost function, even for a strict subclass of submodular cost functions.

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arXiv2022

"Who Is Next in Line?'' On the Significance of Knowing the Arrival Order in Bayesian Online Settings

We introduce a new measure for the performance of online algorithms in Bayesian settings, where the input is drawn from a known prior, but the realizations are revealed one-by-one in an online fashion. Our new measure is called order-competitive ratio. It is defined as the worst case (over all distribution sequences) ratio between the performance of the best order-unaware and order-aware algorithms, and quantifies the loss that is incurred due to lack of knowledge of the arrival order. Despite the growing interest in the role of the arrival order on the performance of online algorithms, this loss has been overlooked thus far. We study the order-competitive ratio in the paradigmatic prophet inequality problem, for the two common objective functions of (i) maximizing the expected value, and (ii) maximizing the probability of obtaining the largest value; and with respect to two families of algorithms, namely (i) adaptive algorithms, and (ii) single-threshold algorithms. We provide tight bounds for all four combinations, with respect to deterministic algorithms. Our analysis requires new ideas and departs from standard techniques. In particular, our adaptive algorithms inevitably go beyond single-threshold algorithms. The results with respect to the order-competitive ratio measure capture the intuition that adaptive algorithms are stronger than single-threshold ones, and may lead to a better algorithmic advice than the classical competitive ratio measure.

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