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Shai Vardi

Publications and source records attributed to Shai Vardi.

17 recordsLinked to original sources

Epistemic Warrant for LLM Recommendations: Characterizing the Basis for Reliance When Ground Truth Is Unavailable

Large language models are increasingly used to support organizational decisions, yet users often lack a principled basis for assessing whether to rely on a specific recommendation. Existing approaches typically evaluate broad model properties, such as reliability, uncertainty, or robustness, or focus on user trust, rather than the underlying basis for relying on an individual recommendation. Adapting theoretical foundations from epistemology, we introduce epistemic warrant, a decision-level construct that characterizes the stability of a model's preference and the scope over which that preference holds. We operationalize this construct through a four-tier reliance certificate for pairwise recommendations, distinguishing among unstable, context-dependent, locally supported, and broadly supported recommendations. We validate the construct using contemporary methodologies: known-groups tests successfully recover expert-prespecified warrant orderings, and stronger warrants systematically align with independent consensus from crowd workers. Furthermore, we demonstrate that epistemic warrant provides information distinct from verbalized confidence and is not readily explained by decision difficulty. Ultimately, this framework offers a theoretically grounded, implementable approach for characterizing the warrant of individual LLM recommendations when objective ground truth is unavailable.

cs.AI

Efficiency, Envy, and Incentives in Combinatorial Assignment

Ensuring efficiency and envy-freeness in allocating indivisible goods without money often requires randomization. However, existing combinatorial assignment mechanisms (for applications such as course allocation, food banks, and refugee resettlement) guarantee these properties either ex ante or ex post, but not both. We propose a new class of mechanisms based on Competitive Equilibrium from Random Incomes (CERI): Agents receive random token budgets and select optimal lotteries at competitive prices that clear markets in expectation. Our main insight is to let the CERI price vector guide all ex-post allocations. We show that all ordinally efficient allocations are CERI allocations, which can be implemented as lotteries over near-feasible Pareto-efficient outcomes. With identical budget distributions, CERI allocations are ordinally envy-free; with budget distributions on small supports, ex-post allocations are envy-free up to one good. Moreover, we design an asymptotically efficient implementation of CERI that satisfies a strong new non-manipulability property in large markets.

econ.TH

Fragile Preferences: A Deep Dive Into Order Effects in Large Language Models

Large language models (LLMs) are increasingly deployed in decision-support systems for high-stakes domains such as hiring and university admissions, where choices often involve selecting among competing alternatives. While prior work has noted position biases in LLM-driven comparisons, these biases have not been systematically analyzed or linked to underlying preference structures. We present the first comprehensive study of position biases across multiple LLMs and two distinct domains: resume comparisons, representing a realistic high-stakes context, and color selection, which isolates position effects by removing confounding factors. We find strong and consistent order effects, including a quality-dependent shift: when all options are high quality, models favor the first option, but when quality is lower, they favor later options. We also identify a previously undocumented bias: a name bias, where certain names are favored despite controlling for demographic signals. To separate superficial tie-breaking from genuine distortions of judgment, we extend the rational choice framework to classify pairwise preferences as robust, fragile, or indifferent. Using this framework, we show that order effects can lead models to select strictly inferior options. These results indicate that LLMs exhibit distinct failure modes not documented in human decision-making. We also propose targeted mitigation strategies, including a novel use of the temperature parameter, to recover underlying preferences when order effects distort model behavior.

cs.AI

Dynamic Combinatorial Assignment

We study a model of dynamic combinatorial assignment of indivisible objects without money. We introduce a new solution concept called ``dynamic approximate competitive equilibrium from equal incomes'' (DACEEI), which stipulates that markets must approximately clear in almost all time periods. A naive repeated application of approximate competitive equilibrium from equal incomes (Budish, 2011) does not yield a desirable outcome because the approximation error in market-clearing compounds quickly over time. We therefore develop a new version of the static approximate competitive equilibrium from carefully constructed random budgets which ensures that, in expectation, markets clear exactly. We then use it to design the ``online combinatorial assignment mechanism'' (OCAM) which implements a DACEEI with high probability. The OCAM is (i) group-strategyproof up to one object (ii) envy-free up to one object for almost all agents (iii) approximately market-clearing in almost all periods with high probability when the market is large and arrivals are random. Applications include refugee resettlement, daycare assignment, and airport slot allocation.

econ.TH

Communication-Aware Scheduling of Precedence-Constrained Tasks on Related Machines

Scheduling precedence-constrained tasks is a classical problem that has been studied for more than fifty years. However, little progress has been made in the setting where there are communication delays between tasks. Results for the case of identical machines were derived nearly thirty years ago, and yet no results for related machines have followed. In this work, we propose a new scheduler, Generalized Earliest Time First (GETF), and provide the first provable, worst-case approximation guarantees for the goals of minimizing both the makespan and total weighted completion time of tasks with precedence constraints on related machines with machine-dependent communication times.

cs.PF

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.

cs.GT

A Parallelizable Acceleration Framework for Packing Linear Programs

This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be used as a black box to speed up linear programming solvers dramatically, by two orders of magnitude in our experiments. We present worst-case guarantees on the quality of the solution and the speedup provided by the algorithm, showing that the framework provides an approximately optimal solution while running the original solver on a much smaller problem. The framework can be used to accelerate exact solvers, approximate solvers, and parallel/distributed solvers. Further, it can be used for both linear programs and integer linear programs.

math.OC

Randomly coloring graphs of bounded treewidth

We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\Delta$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if $k\geq(1+\epsilon)\Delta$, for any $\epsilon>0$.

cs.DS

A note on the size of query trees

We consider query trees of graphs with degree bounded by a constant, $d$. We give simple proofs that the size of a query tree is constant in expectation and $2^{O(d)}\log{n}$ w.h.p.

cs.DS

On the Probe Complexity of Local Computation Algorithms

The Local Computation Algorithms (LCA) model is a computational model aimed at problem instances with huge inputs and output. For graph problems, the input graph is accessed using probes: strong probes (SP) specify a vertex $v$ and receive as a reply a list of $v$'s neighbors, and weak probes (WP) specify a vertex $v$ and a port number $i$ and receive as a reply $v$'s $i^{th}$ neighbor. Given a local query (e.g., "is a certain vertex in the vertex cover of the input graph?"), an LCA should compute the corresponding local output (e.g., "yes" or "no") while making only a small number of probes, with the requirement that all local outputs form a single global solution (e.g., a legal vertex cover). We study the probe complexity of LCAs that are required to work on graphs that may have arbitrarily large degrees. In particular, such LCAs are expected to probe the graph a number of times that is significantly smaller than the maximum, average, or even minimum degree. For weak probes, we focus on the weak coloring problem. Among our results we show a separation between weak 3-coloring and weak 2-coloring for deterministic LCAs: $\log^* n + O(1)$ weak probes suffice for weak 3-coloring, but $\Omega\left(\frac{\log n}{\log\log n}\right)$ weak probes are required for weak 2-coloring. For strong probes, we consider randomized LCAs for vertex cover and maximal/maximum matching. Our negative results include showing that there are graphs for which finding a \emph{maximal} matching requires $\Omega(\sqrt{n})$ strong probes. On the positive side, we design a randomized LCA that finds a $(1-\epsilon)$ approximation to \emph{maximum} matching in regular graphs, and uses $\frac{1}{\epsilon }^{O\left( \frac{1}{\epsilon ^2}\right)}$ probes, independently of the number of vertices and of their degrees.

cs.DS

New Techniques and Tighter Bounds for Local Computation Algorithms

Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Mansour et al., (2012), had previously shown how to convert certain online algorithms to LCAs. In this work, we expand on that line of work and develop new techniques for designing LCAs and bounding their space and time complexity. Our contributions are fourfold: (1) We significantly improve the running times and space requirements of LCAs for previous results, (2) we expand and better define the family of online algorithms which can be converted to LCAs using our techniques, (3) we show that our results apply to a larger family of graphs than that of previous results, and (4) our proofs are simpler and more concise than the previous proof methods. For example, we show how to construct LCAs that require $O(\log{n}\log\log{n})$ space and $O(\log^2{n})$ time (and expected time $O(\log\log{n})$) for problems such as maximal matching on a large family of graphs, as opposed to the henceforth best results that required $O(\log^3{n})$ space and $O(\log^4{n})$ time, and applied to a smaller family of graphs.

cs.DS

The secretary returns

In the online random-arrival model, an algorithm receives a sequence of n requests that arrive in a random order. The algorithm is expected to make an irrevocable decision with regard to each request based only on the observed history. We consider the following natural extension of this model: each request arrives k times, and the arrival order is a random permutation of the kn arrivals; the algorithm is expected to make a decision regarding each request only upon its last arrival. We focus primarily on the case when k=2, which can also be interpreted as each request arriving at, and departing from the system, at a random time. We examine the secretary problem: the problem of selecting the best secretary when the secretaries are presented online according to a random permutation. We show that when each secretary arrives twice, we can achieve a competitive ratio of ~0.768 (compared to 1/e in the classical secretary problem), and that it is optimal. We also show that without any knowledge about the number of secretaries or their arrival times, we can still hire the best secretary with probability at least 2/3, in contrast to the impossibility of achieving a constant success probability in the classical setting. We extend our results to the matroid secretary problem, introduced by Babaioff et al., (2007) and show a simple algorithm that achieves a 2-approximation to the maximal weighted basis in the new model (for k=2). We show that this approximation factor can be improved in special cases of the matroid secretary problem; in particular, we give a 16/9-competitive algorithm for the returning edge-weighted bipartite matching problem.

cs.DS

Local computation mechanism design

We introduce the notion of Local Computation Mechanism Design - designing game theoretic mechanisms which run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. In addition, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanisms need to maintain incentive compatibility with respect to the allocation and payments. We present local computation mechanisms for a variety of classical game-theoretical problems: 1. stable matching, 2. job scheduling, 3. combinatorial auctions for unit-demand and k-minded bidders, and 4. the housing allocation problem. For stable matching, some of our techniques may have general implications. Specifically, we show that when the men's preference lists are bounded, we can achieve an arbitrarily good approximation to the stable matching within a fixed number of iterations of the Gale-Shapley algorithm.

cs.GT

Converting online algorithms to local computation algorithms

We propose a general method for converting online algorithms to local computation algorithms by selecting a random permutation of the input, and simulating running the online algorithm. We bound the number of steps of the algorithm using a query tree, which models the dependencies between queries. We improve previous analyses of query trees on graphs of bounded degree, and extend the analysis to the cases where the degrees are distributed binomially, and to a special case of bipartite graphs. Using this method, we give a local computation algorithm for maximal matching in graphs of bounded degree, which runs in time and space O(log^3 n). We also show how to convert a large family of load balancing algorithms (related to balls and bins problems) to local computation algorithms. This gives several local load balancing algorithms which achieve the same approximation ratios as the online algorithms, but run in O(log n) time and space. Finally, we modify existing local computation algorithms for hypergraph 2-coloring and k-CNF and use our improved analysis to obtain better time and space bounds, of O(log^4 n), removing the dependency on the maximal degree of the graph from the exponent.

cs.DS

Space-efficient Local Computation Algorithms

Recently Rubinfeld et al. (ICS 2011, pp. 223--238) proposed a new model of sublinear algorithms called \emph{local computation algorithms}. In this model, a computation problem $F$ may have more than one legal solution and each of them consists of many bits. The local computation algorithm for $F$ should answer in an online fashion, for any index $i$, the $i^{\mathrm{th}}$ bit of some legal solution of $F$. Further, all the answers given by the algorithm should be consistent with at least one solution of $F$. In this work, we continue the study of local computation algorithms. In particular, we develop a technique which under certain conditions can be applied to construct local computation algorithms that run not only in polylogarithmic time but also in polylogarithmic \emph{space}. Moreover, these local computation algorithms are easily parallelizable and can answer all parallel queries consistently. Our main technical tools are pseudorandom numbers with bounded independence and the theory of branching processes.

cs.DS

Fast Local Computation Algorithms

For input $x$, let $F(x)$ denote the set of outputs that are the "legal" answers for a computational problem $F$. Suppose $x$ and members of $F(x)$ are so large that there is not time to read them in their entirety. We propose a model of {\em local computation algorithms} which for a given input $x$, support queries by a user to values of specified locations $y_i$ in a legal output $y \in F(x)$. When more than one legal output $y$ exists for a given $x$, the local computation algorithm should output in a way that is consistent with at least one such $y$. Local computation algorithms are intended to distill the common features of several concepts that have appeared in various algorithmic subfields, including local distributed computation, local algorithms, locally decodable codes, and local reconstruction. We develop a technique, based on known constructions of small sample spaces of $k$-wise independent random variables and Beck's analysis in his algorithmic approach to the Lov{\'{a}}sz Local Lemma, which under certain conditions can be applied to construct local computation algorithms that run in {\em polylogarithmic} time and space. We apply this technique to maximal independent set computations, scheduling radio network broadcasts, hypergraph coloring and satisfying $k$-SAT formulas.

cs.DS