Aleksandrs Slivkins

Metric embeddings with relaxed guarantees

We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, which achieved striking empirical success at embedding Internet latencies with low distortion into low-dimensional Euclidean space, provided that some small slack is allowed. Answering an open question of Kleinberg, Slivkins, and Wexler (2004), we show that provable guarantees of this type can in fact be achieved in general: any finite metric can be embedded, with constant slack and constant distortion, into constant-dimensional Euclidean space. We then show that there exist stronger embeddings into /spl lscr//sub 1/ which exhibit gracefully degrading distortion: these is a single embedding into /spl lscr//sub 1/ that achieves distortion at most O(log 1//spl epsi/) on all but at most an /spl epsi/ fraction of distances, simultaneously for all /spl epsi/ > 0. We extend this with distortion O(log 1//spl epsi/)/sup 1/p/ to maps into general /spl lscr//sub p/, p /spl ges/ 1 for several classes of metrics, including those with bounded doubling dimension and those arising from the shortest-path metric of a graph with an excluded minor. Finally, we show that many of our constructions are tight, and give a general technique to obtain lower bounds for /spl epsi/-slack embeddings from lower bounds for low-distortion embeddings.

Truthful mechanisms with implicit payment computation

It is widely believed that computing payments needed to induce truthful bidding is somehow harder than simply computing the allocation. We show that the opposite is true for single-parameter domains: creating a randomized truthful mechanism is essentially as easy as a single call to a monotone allocation function. Our main result is a general procedure to take a monotone allocation rule and transform it (via a black-box reduction) into a randomized mechanism that is truthful in expectation and individually rational for every realization. Moreover, the mechanism implements the same outcome as the original allocation rule with probability arbitrarily close to 1, and requires evaluating that allocation rule only once. Because our reduction is simple, versatile, and general, it has many applications to mechanism design problems in which re-evaluating the allocation function is either burdensome or informationally impossible. Applying our result to the multi-armed bandit problem, we obtain truthful randomized mechanisms whose regret matches the information-theoretic lower bound up to logarithmic factors, even though prior work showed this is impossible for truthful deterministic mechanisms. We also present applications to offline mechanism design, showing that randomization can circumvent a communication complexity lower bound for deterministic payments computation, and that it can also be used to create truthful shortest path auctions that approximate the welfare of the VCG allocation arbitrarily well, while having the same running time complexity as Dijkstras algorithm.

Characterizing Truthful Multi-armed Bandit Mechanisms

We consider a multiround auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneers goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the multi-armed bandit problem, and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by regret, the difference in social welfare between the algorithm and the benchmark which always selects the same “best” advertisement. We investigate how the design of multi-armed bandit algorithms is affecte...

Incentivizing High Quality Crowdwork

We study the causal effects of financial incentives on the quality of crowdwork. We focus on performance-based payments (PBPs), bonus payments awarded to workers for producing high quality work. We design and run randomized behavioral experiments on the popular crowdsourcing platform Amazon Mechanical Turk with the goal of understanding when, where, and why PBPs help, identifying properties of the payment, payment structure, and the task itself that make them most effective. We provide examples of tasks for which PBPs do improve quality. For such tasks, the effectiveness of PBPs is not too sensitive to the threshold for quality required to receive the bonus, while the magnitude of the bonus must be large enough to make the reward salient. We also present examples of tasks for which PBPs do not improve quality. Our results suggest that for PBPs to improve quality, the task must be effort-responsive: the task must allow workers to produce higher quality work by exerting more effort. We also give a simple method to determine if a task is effort-responsive a priori. Furthermore, our experiments suggest that all payments on Mechanical Turk are, to some degree, implicitly performance-based in that workers believe their work may be rejected if their performance is sufficiently poor. In the full version of this paper, we propose a new model of worker behavior that extends the standard principal-agent model from economics to include a workers subjective beliefs about his likelihood of being paid, and show that the predictions of this model are in line with our experimental findings. This model may be useful as a foundation for theoretical studies of incentives in crowdsourcing markets.

Triangulation and embedding using small sets of beacons

Concurrent with recent theoretical interest in the problem of metric embedding, a growing body of research in the networking community has studied the distance matrix defined by node-to-node latencies in the Internet, resulting in a number of recent approaches that approximately embed this distance matrix into low-dimensional Euclidean space. Here we give algorithms with provable performance guarantees for beacon-based triangulation and embedding. We show that in addition to multiplicative error in the distances, performance guarantees for beacon-based algorithms typically must include a notion of slack - a certain fraction of all distances may be arbitrarily distorted. For metrics of bounded doubling dimension (which have been proposed as a reasonable abstraction of Internet latencies), we show that triangulation-based reconstruction with a constant number of beacons can achieve multiplicative error 1 + /spl delta/ on a 1 - /spl epsiv/ fraction of distances, for arbitrarily small constants /spl delta/ and /spl epsiv/. For this same class of metrics, we give a beacon-based embedding algorithm that achieves constant distortion on a 1 - /spl epsiv/ fraction of distances; this provides some theoretical justification for the success of the recent global network positioning algorithm of Ng and Zhang, and it forms an interesting contrast with lower bounds showing that it is not possible to embed all distances in a doubling metric with constant distortion. We also give results for other classes of metrics, as well as distributed algorithms that require only a sparse set of distances but do not place too much measurement load on any one node.

Parameterized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs

Given a graph and pairs s i t i of terminals, the edge-disjoint paths problem is to determine whether there exist s i t i paths that do not share any edges. We consider this problem on acyclic digraphs. It is known to be NP-complete and solvable in time n O(k) where k is the number of paths. It has been a long-standing open question whether it is fixed-parameter tractable in k. We resolve this question in the negative: we show that the problem is W[1]-hard. In fact it remains W[1]-hard even if the demand graph consists of two sets of parallel edges.

Metric Embeddings with Relaxed Guarantees

We consider the problem of embedding finite metrics with slack: We seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, which achieved striking empirical success at embedding Internet latencies with low distortion into low-dimensional Euclidean space, provided that some small slack is allowed. Answering an open question of Kleinberg, Slivkins, and Wexler [in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004], we show that provable guarantees of this type can in fact be achieved in general: Any finite metric space can be embedded, with constant slack and constant distortion, into constant-dimensional Euclidean space. We then show that there exist stronger embeddings into

Incentivizing high quality crowdwork

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Interleaving schemes on circulant graphs with two offsets

which exhibit gracefully degrading distortion: There is a single embedding into

Selection and influence in cultural dynamics

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