arXiv subjects

Parnian Shahkar

Publications and source records attributed to Parnian Shahkar.

9 recordsLinked to original sources

arXiv2025

Human-AI Collaboration with Misaligned Preferences

In many real-life settings, algorithms play the role of assistants, while humans ultimately make the final decision. Often, algorithms specifically act as curators, narrowing down a wide range of options into a smaller subset that the human picks between: consider content recommendation or chatbot responses to questions with multiple valid answers. Crucially, humans may not know their own preferences perfectly either, but instead may only have access to a noisy sampling over preferences. Algorithms can assist humans by curating a smaller subset of items, but must also face the challenge of misalignment: humans may have different preferences from each other (and from the algorithm), and the algorithm may not know the exact preferences of the human they are facing at any point in time. In this paper, we model and theoretically study such a setting. Specifically, we show instances where humans benefit by collaborating with a misaligned algorithm. Surprisingly, we show that humans gain more utility from a misaligned algorithm (which makes different mistakes) than from an aligned algorithm. Next, we build on this result by studying what properties of algorithms maximize human welfare when the goals could be either utilitarian welfare or ensuring all humans benefit. We conclude by discussing implications for designers of algorithmic tools and policymakers.

cs.GT↗

arXiv2025

Robust Popular Matchings

We study popularity for matchings under preferences. This solution concept captures matchings that do not lose against any other matching in a majority vote by the agents. A popular matching is said to be robust if it is popular among multiple instances. We present a polynomial-time algorithm for deciding whether there exists a robust popular matching if instances only differ with respect to the preferences of a single agent. The same method applies also to dominant matchings, a subclass of maximum-size popular matchings. By contrast, we obtain NP-completeness if two instances differ only by two agents of the same side or by a swap of two adjacent alternatives by two agents. The first hardness result applies to dominant matchings as well. Moreover, we find another complexity dichotomy based on preference completeness for the case where instances differ by making some options unavailable. We conclude by discussing related models, such as strong and mixed popularity.

cs.DS↗

arXiv2025

The Complexity of Finding Local Optima in Contrastive Learning

Contrastive learning is a powerful technique for discovering meaningful data representations by optimizing objectives based on $\textit{contrastive information}$, often given as a set of weighted triplets $\{(x_i, y_i^+, z_{i}^-)\}_{i = 1}^m$ indicating that an "anchor" $x_i$ is more similar to a "positive" example $y_i$ than to a "negative" example $z_i$. The goal is to find representations (e.g., embeddings in $\mathbb{R}^d$ or a tree metric) where anchors are placed closer to positive than to negative examples. While finding $\textit{global}$ optima of contrastive objectives is $\mathsf{NP}$-hard, the complexity of finding $\textit{local}$ optima -- representations that do not improve by local search algorithms such as gradient-based methods -- remains open. Our work settles the complexity of finding local optima in various contrastive learning problems by proving $\mathsf{PLS}$-hardness in discrete settings (e.g., maximize satisfied triplets) and $\mathsf{CLS}$-hardness in continuous settings (e.g., minimize Triplet Loss), where $\mathsf{PLS}$ (Polynomial Local Search) and $\mathsf{CLS}$ (Continuous Local Search) are well-studied complexity classes capturing local search dynamics in discrete and continuous optimization, respectively. Our results imply that no polynomial time algorithm (local search or otherwise) can find a local optimum for various contrastive learning problems, unless $\mathsf{PLS}\subseteq\mathsf{P}$ (or $\mathsf{CLS}\subseteq \mathsf{P}$ for continuous problems). Even in the unlikely scenario that $\mathsf{PLS}\subseteq\mathsf{P}$ (or $\mathsf{CLS}\subseteq \mathsf{P}$), our reductions imply that there exist instances where local search algorithms need exponential time to reach a local optimum, even for $d=1$ (embeddings on a line).

cs.LG↗

arXiv2025

On the Existence and Complexity of Core-Stable Data Exchanges

The rapid growth of data-driven technologies and the emergence of various data-sharing paradigms have underscored the need for efficient and stable data exchange protocols. In any such exchange, agents must carefully balance the benefit of acquiring valuable data against the cost of sharing their own. Ensuring stability in these exchanges is essential to prevent agents -- or groups of agents -- from departing and conducting local (and potentially more favorable) exchanges among themselves. To address this, we study a model where agents participate in a data exchange. Each agent has an associated payoff for the data acquired from other agents and a cost incurred during sharing its own data. The net utility of an agent is payoff minus the cost. We adapt the classical notion of core-stability from cooperative game theory to data exchange. A data exchange is core-stable if no subset of agents has any incentive to deviate to a different exchange. We show that a core-stable data exchange is guaranteed to exist when agents have concave payoff functions and convex cost functions -- a setting typical in domains like PAC learning and random discovery models. We show that relaxing either of the foregoing conditions may result in the nonexistence of core-stable data exchanges. Then, we prove that finding a core-stable exchange is PPAD-hard, even when the potential blocking coalitions are restricted to constant size. To the best of our knowledge, this provides the first known PPAD-hardness result for core-like guarantees in data economics. Finally, we show that data exchange can be modelled as a balanced $n$-person game. This immediately gives a pivoting algorithm via Scarf's theorem \cite{Scarf1967core}. We show that the pivoting algorithm works well in practice through our empirical results.

cs.GT↗

arXiv2025

Effects of Vote Delegation in Blockchains: Who Wins?

This paper investigates which alternative benefits from vote delegation in binary collective decisions within blockchains. We begin by examining two extreme cases of voting weight distributions: Equal-Weight (EW), where each voter has equal voting weight, and Dominant-Weight (DW), where a single voter holds a majority of the voting weights before any delegation occurs. We show that vote delegation tends to benefit the ex-ante minority under EW, i.e., the alternative with a lower initial probability of winning. The converse holds under DW distribution. Through numerical simulations, we extend our findings to arbitrary voting weight distributions, showing that vote delegation benefits the ex-ante majority when it leads to a more balanced distribution of voting weights. Finally, in large communities where all agents have equal voting weight, vote delegation has a negligible impact on the outcome. As a practical consequence, vote delegation can be beneficial for blockchains with highly unbalanced voting rights, but not for those with balanced rights. In decentralized finance (DeFi), vote delegation is widely adopted to streamline governance and increase participation. However, it remains unclear when delegation actually aligns outcomes with community preferences.

cs.GT↗

arXiv2025

Welfare Approximation in Additively Separable Hedonic Games

Partitioning a set of $n$ items or agents while maximizing the value of the partition is a fundamental algorithmic task. We study this problem in the specific setting of maximizing social welfare in additively separable hedonic games. Unfortunately, this task faces strong computational boundaries: Extending previous results, we show that approximating welfare by a factor of $n^{1-ε}$ is NP-hard, even for severely restricted weights. However, we can obtain a randomized $\log n$-approximation on instances for which the sum of input valuations is nonnegative. Finally, we study two stochastic models of aversion-to-enemies games, where the weights are derived from Erdős-Rényi or multipartite graphs. We obtain constant-factor and logarithmic-factor approximations with high probability.

cs.GT↗

arXiv2025

Improved MMS Approximations for Few Agent Types

We study fair division of indivisible goods under the maximin share (MMS) fairness criterion in settings where agents are grouped into a small number of types, with agents within each type having identical valuations. For the special case of a single type, an exact MMS allocation is always guaranteed to exist. However, for two or more distinct agent types, exact MMS allocations do not always exist, shifting the focus to establishing the existence of approximate-MMS allocations. A series of works over the last decade has resulted in the best-known approximation guarantee of $\frac{3}{4} + \frac{3}{3836}$. In this paper, we improve the approximation guarantees for settings where agents are grouped into two or three types, a scenario that arises in many practical settings. Specifically, we present novel algorithms that guarantee a $\frac{4}{5}$-MMS allocation for two agent types and a $\frac{16}{21}$-MMS allocation for three agent types. Our approach leverages the MMS partition of the majority type and adapts it to provide improved fairness guarantees for all types.

cs.GT↗

arXiv2025

Online Fair Division: Towards Ex-Post Constant MMS Guarantees

We investigate the problem of fairly allocating $m$ indivisible items among $n$ sequentially arriving agents with additive valuations, under the sought-after fairness notion of maximin share (MMS). We first observe a strong impossibility: without appropriate knowledge about the valuation functions of the incoming agents, no online algorithm can ensure any non-trivial MMS approximation, even when there are only two agents. Motivated by this impossibility, we introduce OnlineKTypeFD (online $k$-type fair division), a model that balances theoretical tractability with real-world applicability. In this model, each arriving agent belongs to one of $k$ types, with all agents of a given type sharing the same known valuation function. We do not constrain $k$ to be a constant. Upon arrival, an agent reveals her type, receives an irrevocable allocation, and departs. We study the ex-post MMS guarantees of online algorithms under two arrival models: 1- Adversarial arrivals: In this model, an adversary determines the type of each arriving agent. We design a $\frac{1}{k}$-MMS competitive algorithm and complement it with a lower bound, ruling out any $Ω(\frac{1}{\sqrt{k}})$-MMS-competitive algorithm, even for binary valuations. 2- Stochastic arrivals: In this model, the type of each arriving agent is independently drawn from an underlying, possibly unknown distribution. Unlike the adversarial setting where the dependence on $k$ is unavoidable, we surprisingly show that in the stochastic setting, an asymptotic, arbitrarily close-to-$\frac{1}{2}$-MMS competitive guarantee is achievable under mild distributional assumptions. Our results extend naturally to a learning-augmented framework; when given access to predictions about valuation functions, we show that the competitive ratios of our algorithms degrade gracefully with multiplicative prediction errors.

cs.GT↗

arXiv2025

Equitable Core Imputations for Max-Flow, MST and $b$-Matching Games

We study fair allocation of profit (or cost) for three central problems from combinatorial optimization: Max-Flow, MST and $b$-matching. The essentially unequivocal choice of solution concept for this purpose would be the core, because of its highly desirable properties. However, recent work [Vaz24] observed that for the assignment game, an arbitrary core imputation makes no fairness guarantee at the level of individual agents. To rectify this deficiency, special core imputations, called equitable core imputations, were defined - there are two such imputations, leximin and leximax - and efficient algorithms were given for finding them. For all three games, we start by giving examples to show that an arbitrary core imputation can be excessively unfair to certain agents. This led us to seek equitable core imputations for our three games as well. However, the ubiquitous tractable vs intractable schism separates the assignment game from our three games, making our task different from that of [Vaz24]. As is usual in the presence of intractability, we resorted to defining the Owen set for each game and algorithmically relating it to the set of optimal dual solutions of the underlying combinatorial problem. We then give polynomial time algorithms for finding equitable imputations in the Owen set. The motivation for this work is two-fold: the emergence of automated decision-making, with a special emphasis on fairness, and the plethora of industrial applications of our three games.

cs.GT↗