arXiv subjects

Alexandros Psomas

Publications and source records attributed to Alexandros Psomas.

33 records · Page 2Linked to original sources

arXiv2024

Fair and Efficient Allocations Without Obvious Manipulations

We consider the fundamental problem of allocating a set of indivisible goods among strategic agents with additive valuation functions. It is well known that, in the absence of monetary transfers, Pareto efficient and truthful rules are dictatorial, while there is no deterministic truthful mechanism that allocates all items and achieves envy-freeness up to one item (EF1), even for the case of two agents. In this paper, we investigate the interplay of fairness and efficiency under a relaxation of truthfulness called non-obvious manipulability (NOM), recently proposed by Troyan and Morrill. We show that this relaxation allows us to bypass the aforementioned negative results in a very strong sense. Specifically, we prove that there are deterministic and EF1 algorithms that are not obviously manipulable, and the algorithm that maximizes utilitarian social welfare (the sum of agents' utilities), which is Pareto efficient but not dictatorial, is not obviously manipulable for $n \geq 3$ agents (but obviously manipulable for $n=2$ agents). At the same time, maximizing the egalitarian social welfare (the minimum of agents' utilities) or the Nash social welfare (the product of agents' utilities) is obviously manipulable for any number of agents and items. Our main result is an approximation preserving black-box reduction from the problem of designing EF1 and NOM mechanisms to the problem of designing EF1 algorithms. En route, we prove an interesting structural result about EF1 allocations, as well as new "best-of-both-worlds" results (for the problem without incentives), that might be of independent interest.

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arXiv2023

On the Robustness of Mechanism Design under Total Variation Distance

We study the problem of designing mechanisms when agents' valuation functions are drawn from unknown and correlated prior distributions. In particular, we are given a prior distribution $\D$, and we are interested in designing a (truthful) mechanism that has good performance for all ``true distributions'' that are close to $\D$ in Total Variation (TV) distance. We show that DSIC and BIC mechanisms in this setting are strongly robust with respect to TV distance, for any bounded objective function $\Ocal$, extending a recent result of Brustle et al. (\cite{Brustle2020}, EC 2020). At the heart of our result is a fundamental duality property of total variation distance. As direct applications of our result, we (i) demonstrate how to find approximately revenue-optimal and approximately BIC mechanisms for weakly dependent prior distributions; (ii) show how to find correlation-robust mechanisms when only ``noisy'' versions of marginals are accessible, extending recent results of Bei et. al. (\cite{bei2019correlation}, SODA 2019); (iii) prove that prophet-inequality type guarantees are preserved for correlated priors, recovering a variant of a result of D{ü}tting and Kesselheim (\cite{Dutting19}, EC 2019); (iv) give a new necessary condition for a correlated distribution to witness an infinite separation in revenue between simple and optimal mechanisms, complementing recent results of Psomas et al. (\cite{psomas2022infinite}, NeurIPS 2022); (v) give a new condition for simple mechanisms to approximate revenue-optimal mechanisms for the case of a single agent whose type is drawn from a correlated distribution that can be captured by a Markov Random Field, complementing recent results of Cai and Oikonomou (\cite{Cai21}, EC 2021).

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arXiv2023

Refined Mechanism Design for Approximately Structured Priors via Active Regression

We consider the problem of a revenue-maximizing seller with a large number of items $m$ for sale to $n$ strategic bidders, whose valuations are drawn independently from high-dimensional, unknown prior distributions. It is well-known that optimal and even approximately-optimal mechanisms for this setting are notoriously difficult to characterize or compute, and, even when they can be found, are often rife with various counter-intuitive properties. In this paper, following a model introduced recently by Cai and Daskalakis~\cite{cai2022recommender}, we consider the case that bidders' prior distributions can be well-approximated by a topic model. We design an active learning component, responsible for interacting with the bidders and outputting low-dimensional approximations of their types, and a mechanism design component, responsible for robustifying mechanisms for the low-dimensional model to work for the approximate types of the former component. On the active learning front, we cast our problem in the framework of Randomized Linear Algebra (RLA) for regression problems, allowing us to import several breakthrough results from that line of research, and adapt them to our setting. On the mechanism design front, we remove many restrictive assumptions of prior work on the type of access needed to the underlying distributions and the associated mechanisms. To the best of our knowledge, our work is the first to formulate connections between mechanism design, and RLA for active learning of regression problems, opening the door for further applications of randomized linear algebra primitives to mechanism design.

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arXiv2023

Fairly Allocating Goods in Parallel

We initiate the study of parallel algorithms for fairly allocating indivisible goods among agents with additive preferences. We give fast parallel algorithms for various fundamental problems, such as finding a Pareto Optimal and EF1 allocation under restricted additive valuations, finding an EF1 allocation for up to three agents, and finding an envy-free allocation with subsidies. On the flip side, we show that fast parallel algorithms are unlikely to exist (formally, $CC$-hard) for the problem of computing Round-Robin EF1 allocations.

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arXiv2023

Smoothed Analysis of Social Choice, Revisited

A canonical problem in social choice is how to aggregate ranked votes: given $n$ voters' rankings over $m$ candidates, what voting rule $f$ should we use to aggregate these votes into a single winner? One standard method for comparing voting rules is by their satisfaction of axioms - properties that we want a "reasonable" rule to satisfy. Unfortunately, this approach leads to several impossibilities: no voting rule can simultaneously satisfy all the properties we want, at least in the worst case over all possible inputs. Motivated by this, we consider a relaxation of these worst case requirements. We do so using a "smoothed" model of social choice, where votes are perturbed with small amounts of noise. If, no matter which input profile we start with, the probability (post-noise) of an axiom being satisfied is large, we will consider the axiom as good as satisfied - called "smoothed-satisfied" - even if it may be violated in the worst case. Our model is a mild restriction of Lirong Xia's, and corresponds closely to that in Spielman and Teng's original work on smoothed analysis. Much work has been done so far in several papers by Xia on axiom satisfaction under such noise. In our paper, we aim to give a more cohesive overview on when smoothed analysis of social choice is useful. Within our model, we give simple sufficient conditions for smoothed-satisfaction or smoothed-violation of several previously-unstudied axioms and paradoxes, plus many of those studied by Xia. We then observe that, in a practically important subclass of noise models, although convergence eventually occurs, known rates may require an extremely large number of voters. Motivated by this, we prove bounds specifically within a canonical noise model from this subclass - the Mallows model. Here, we present a more nuanced picture on exactly when smoothed analysis can help.

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arXiv2023

On the Existence of Envy-Free Allocations Beyond Additive Valuations

We study the problem of fairly allocating $m$ indivisible items among $n$ agents. Envy-free allocations, in which each agent prefers her bundle to the bundle of every other agent, need not exist in the worst case. However, when agents have additive preferences and the value $v_{i,j}$ of agent $i$ for item $j$ is drawn independently from a distribution $D_i$, envy-free allocations exist with high probability when $m \in Ω( n \log n / \log \log n )$. In this paper, we study the existence of envy-free allocations under stochastic valuations far beyond the additive setting. We introduce a new stochastic model in which each agent's valuation is sampled by first fixing a worst-case function, and then drawing a uniformly random renaming of the items, independently for each agent. This strictly generalizes known settings; for example, $v_{i,j} \sim D_i$ may be seen as picking a random (instead of a worst-case) additive function before renaming. We prove that random renaming is sufficient to ensure that envy-free allocations exist with high probability in very general settings. When valuations are non-negative and ``order-consistent,'' a valuation class that generalizes additive, budget-additive, unit-demand, and single-minded agents, SD-envy-free allocations (a stronger notion of fairness than envy-freeness) exist for $m \in ω(n^2)$ when $n$ divides $m$, and SD-EFX allocations exist for all $m \in ω(n^2)$. The dependence on $n$ is tight, that is, for $m \in O(n^2)$ envy-free allocations don't exist with constant probability. For the case of arbitrary valuations (allowing non-monotone, negative, or mixed-manna valuations) and $n=2$ agents, we prove envy-free allocations exist with probability $1 - Θ(1/m)$ (and this is tight).

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arXiv2023

Reward Selection with Noisy Observations

We study a fundamental problem in optimization under uncertainty. There are $n$ boxes; each box $i$ contains a hidden reward $x_i$. Rewards are drawn i.i.d. from an unknown distribution $\mathcal{D}$. For each box $i$, we see $y_i$, an unbiased estimate of its reward, which is drawn from a Normal distribution with known standard deviation $σ_i$ (and an unknown mean $x_i$). Our task is to select a single box, with the goal of maximizing our reward. This problem captures a wide range of applications, e.g. ad auctions, where the hidden reward is the click-through rate of an ad. Previous work in this model [BKMR12] proves that the naive policy, which selects the box with the largest estimate $y_i$, is suboptimal, and suggests a linear policy, which selects the box $i$ with the largest $y_i - c \cdot σ_i$, for some $c > 0$. However, no formal guarantees are given about the performance of either policy (e.g., whether their expected reward is within some factor of the optimal policy's reward). In this work, we prove that both the naive policy and the linear policy are arbitrarily bad compared to the optimal policy, even when $\mathcal{D}$ is well-behaved, e.g. has monotone hazard rate (MHR), and even under a "small tail" condition, which requires that not too many boxes have arbitrarily large noise. On the flip side, we propose a simple threshold policy that gives a constant approximation to the reward of a prophet (who knows the realized values $x_1, \dots, x_n$) under the same "small tail" condition. We prove that when this condition is not satisfied, even an optimal clairvoyant policy (that knows $\mathcal{D}$) cannot get a constant approximation to the prophet, even for MHR distributions, implying that our threshold policy is optimal against the prophet benchmark, up to constants.

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arXiv2022

Simple Mechanisms for Welfare Maximization in Rich Advertising Auctions

Internet ad auctions have evolved from a few lines of text to richer informational layouts that include images, sitelinks, videos, etc. Ads in these new formats occupy varying amounts of space, and an advertiser can provide multiple formats, only one of which can be shown. The seller is now faced with a multi-parameter mechanism design problem. Computing an efficient allocation is computationally intractable, and therefore the standard Vickrey-Clarke-Groves (VCG) auction, while truthful and welfare-optimal, is impractical. In this paper, we tackle a fundamental problem in the design of modern ad auctions. We adopt a ``Myersonian'' approach and study allocation rules that are monotone both in the bid and set of rich ads. We show that such rules can be paired with a payment function to give a truthful auction. Our main technical challenge is designing a monotone rule that yields a good approximation to the optimal welfare. Monotonicity doesn't hold for standard algorithms, e.g. the incremental bang-per-buck order, that give good approximations to ``knapsack-like'' problems such as ours. In fact, we show that no deterministic monotone rule can approximate the optimal welfare within a factor better than $2$ (while there is a non-monotone FPTAS). Our main result is a new, simple, greedy and monotone allocation rule that guarantees a $3$ approximation. In ad auctions in practice, monotone allocation rules are often paired with the so-called Generalized Second Price (GSP) payment rule, which charges the minimum threshold price below which the allocation changes. We prove that, even though our monotone allocation rule paired with GSP is not truthful, its Price of Anarchy (PoA) is bounded. Under standard no overbidding assumption, we prove a pure PoA bound of $6$ and a Bayes-Nash PoA bound of $\frac{6}{(1 - \frac{1}{e})}$. Finally, we experimentally test our algorithms on real-world data.

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arXiv2022

Beyond Cake Cutting: Allocating Homogeneous Divisible Goods

The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in the Robertson-Webb query model. However, the root of this problem's complexity is somewhat artificial: the agents' values are assumed to be additive across different pieces of the "cake" but infinitely complicated within each piece. This is unrealistic in most of the motivating examples, where the cake represents a finite collection of homogeneous goods. We address this issue by introducing a fair division model that more accurately captures these applications: the value that an agent gains from a given good depends only on the amount of the good they receive, yet it can be an arbitrary function of this amount, allowing the agents to express preferences that go beyond standard cake cutting. In this model, we study the query complexity of computing allocations that are not just envy-free, but also approximately Pareto optimal among all envy-free allocations. Using a novel flow-based approach, we show that we can encode the ex-post feasibility of randomized allocations via a polynomial number of constraints, which reduces our problem to solving a linear program.

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arXiv2020

Hitting the High Notes: Subset Selection for Maximizing Expected Order Statistics

We consider the fundamental problem of selecting $k$ out of $n$ random variables in a way that the expected highest or second-highest value is maximized. This question captures several applications where we have uncertainty about the quality of candidates (e.g. auction bids, search results) and have the capacity to explore only a small subset due to an exogenous constraint. For example, consider a second price auction where system constraints (e.g., costly retrieval or model computation) allow the participation of only $k$ out of $n$ bidders, and the goal is to optimize the expected efficiency (highest bid) or expected revenue (second highest bid). We study the case where we are given an explicit description of each random variable. We give a PTAS for the problem of maximizing the expected highest value. For the second-highest value, we prove a hardness result: assuming the Planted Clique Hypothesis, there is no constant factor approximation algorithm that runs in polynomial time. Surprisingly, under the assumption that each random variable has monotone hazard rate (MHR), a simple score-based algorithm, namely picking the $k$ random variables with the largest $1/\sqrt{k}$ top quantile value, is a constant approximation to the expected highest and second highest value, \emph{simultaneously}.

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arXiv2020

Fair Division with Binary Valuations: One Rule to Rule Them All

We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule -- maximum Nash welfare (MNW) -- provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic tie-breaking is group strategyproof in addition to being envy-free up to one good and Pareto optimal. We also prove that fractional MNW -- known to be group strategyproof, envy-free, and Pareto optimal -- can be implemented as a distribution over deterministic MNW allocations, which are envy-free up to one good. Our work establishes maximum Nash welfare as the ultimate allocation rule in the realm of binary additive preferences.

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arXiv2020

Fair and Efficient Online Allocations with Normalized Valuations

A set of divisible resources becomes available over a sequence of rounds and needs to be allocated immediately and irrevocably. Our goal is to distribute these resources to maximize fairness and efficiency. Achieving any non-trivial guarantees in an adversarial setting is impossible. However, we show that normalizing the agent values, a very common assumption in fair division, allows us to escape this impossibility. Our main result is an online algorithm for the case of two agents that ensures the outcome is envy-free while guaranteeing 91.6% of the optimal social welfare. We also show that this is near-optimal: there is no envy-free algorithm that guarantees more than 93.3% of the optimal social welfare.

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arXiv2020

Fairness-Efficiency Tradeoffs in Dynamic Fair Division

We investigate the tradeoffs between fairness and efficiency when allocating indivisible items over time. Suppose T items arrive over time and must be allocated upon arrival, immediately and irrevocably, to one of n agents. Agent i assigns a value v_{it} in [0,1] to the t-th item to arrive and has an additive valuation function. If the values are chosen by an adaptive adversary it is known that the algorithm that minimizes maximum pairwise envy simply allocates each item uniformly at random; the maximum pairwise envy is then sublinear in T. If the values are independently and identically drawn from an adversarially chosen distribution D, it is also known that, under some mild conditions on D, allocating to the agent with the highest value -- a Pareto efficient allocation -- is envy-free with high probability. In this paper we study fairness-efficiency tradeoffs in this setting and provide matching upper and lower bounds under a spectrum of progressively stronger adversaries. On one hand we show that, even against a non-adaptive adversary, there is no algorithm with sublinear maximum pairwise envy that Pareto dominates the simple algorithm that allocates each item uniformly at random. On the other hand, under a slightly weaker adversary regime where item values are drawn from a known distribution and are independent with respect to time, i.e. v_{it} is independent of v_{it'} but possibly correlated with v_{i't}, optimal (in isolation) efficiency is compatible with optimal (in isolation) fairness. That is, we give an algorithm that is Pareto efficient ex-post and is simultaneously optimal with respect to fairness: for each pair of agents i and j, either i envies j by at most one item (a prominent fairness notion), or $i$ does not envy j with high probability. En route, we prove a structural result about allocations of divisible items that might be of independent interest.

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arXiv2019

Persuasion and Incentives Through the Lens of Duality

Lagrangian duality underlies both classical and modern mechanism design. In particular, the dual perspective often permits simple and detail-free characterizations of optimal and approximately optimal mechanisms. This paper applies this same methodology to a close cousin of traditional mechanism design, one which shares conceptual and technical elements with its more mature relative: the burgeoning field of persuasion. The dual perspective permits us to analyze optimal persuasion schemes both in settings which have been analyzed in prior work, as well as for natural generalizations which we are the first to explore in depth. Most notably, we permit combining persuasion policies with payments, which serve to augment the persuasion power of the scheme. In both single and multi-receiver settings, as well as under a variety of constraints on payments, we employ duality to obtain structural insights, as well as tractable and simple characterizations of optimal policies.

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arXiv2019

How to Hire Secretaries with Stochastic Departures

We study a generalization of the secretary problem, where decisions do not have to be made immediately upon candidates' arrivals. After arriving, each candidate stays in the system for some (random) amount of time and then leaves, whereupon the algorithm has to decide irrevocably whether to select this candidate or not. The goal is to maximize the probability of selecting the best candidate overall. We assume that the arrival and waiting times are drawn from known distributions. Our first main result is a characterization of the optimal policy for this setting. We show that when deciding whether to select a candidate it suffices to know only the time and the number of candidates that have arrived so far. Furthermore, the policy is monotone non-decreasing in the number of candidates seen so far, and, under certain natural conditions, monotone non-increasing in the time. Our second main result is proving that when the number of candidates is large, a single threshold policy is almost optimal.

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