Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation

Bulteau, Laurent; Shahaf, Gal; Shapiro, Ehud; Talmon, Nimrod

doi:10.1613/jair.1.12388

Cited by 5 publications

(3 citation statements)

References 42 publications

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“…A main takeaway from our work is that ill-connected communication topologies can vastly magnify the effect of bad actors. Given that decentralized consensus has been proposed as a backbone for digital democracy (Bulteau et al, 2021), and that decentralized learning is touted to be an alternative to current centralized training paradigms, our findings are significant. A simple strategy we recommend (along with using SCCLIP) is adding random edges in order to improve the connectivity and robustify the network.…”

Section: Discussionmentioning

confidence: 80%

Byzantine-Robust Decentralized Learning via Self-Centered Clipping

He¹,

Karimireddy²,

Jäggi³

2022

Preprint

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In this paper, we study the challenging task of Byzantine-robust decentralized training on arbitrary communication graphs. Unlike federated learning where workers communicate through a server, workers in the decentralized environment can only talk to their neighbors, making it harder to reach consensus. We identify a novel dissensus attack in which few malicious nodes can take advantage of information bottlenecks in the topology to poison the collaboration. To address these issues, we propose a Self-Centered Clipping (SCCLIP) algorithm for Byzantine-robust consensus and optimization, which is the first to provably converge to a O(δ max ζ 2 /γ 2 ) neighborhood of the stationary point for non-convex objectives under standard assumptions. Finally, we demonstrate the encouraging empirical performance of SC-CLIP under a large number of attacks.

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Section: Discussionmentioning

confidence: 80%

Byzantine-Robust Decentralized Learning via Self-Centered Clipping

He¹,

Karimireddy²,

Jäggi³

2022

Preprint

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“…An important feature of their model that sets it somewhat apart from prior work is the presence of a special reference point, i.e., the status quo. The agenda of social choice in the presence of status quo has recently been pursued by Shapiro, Talmon, and coauthors in a series of papers (Shapiro and Talmon 2018;Shahaf, Shapiro, and Talmon 2019;Bulteau et al 2021;Abramowitz, Shapiro, and Talmon 2020).…”

Section: Related Workmentioning

confidence: 99%

Complexity of Deliberative Coalition Formation

Elkind¹,

Ghosh²,

Goldberg³

2022

Preprint

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Elkind et al. (2021Elkind et al. ( , 2020 introduced a model for deliberative coalition formation, where a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. In their model, agents and proposals are points in a metric space, agents' preferences are determined by distances, and agents deliberate by dynamically forming coalitions around proposals that they prefer over the status quo. The deliberation process operates via k-compromise transitions, where agents from k (current) coalitions come together to form a larger coalition in order to support a (perhaps new) proposal, possibly leaving behind some of the dissenting agents from their old coalitions. A deliberation succeeds if it terminates by identifying a proposal with the largest possible support. For deliberation in d dimensions, Elkind et al. consider two variants of their model: in the Euclidean model, proposals and agent locations are points in R d and the distance is measured according to || • ||2; and in the hypercube model, proposals and agent locations are vertices of the d-dimensional hypercube and the metric is the Hamming distance. They show that in the continuous model 2-compromises are guaranteed to succeed, but in the discrete model for deliberation to succeed it may be necessary to use k-compromises with k ≥ d. We complement their analysis by (1) proving that in both models it is hard to find a proposal with a high degree of support, and even a 2-compromise transition may be hard to compute; (2) showing that a sequence of 2-compromise transitions may be exponentially long; (3) strengthening the lower bound on the size of the compromise for the d-hypercube model from d to 2 Ω(d) .

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“…An important feature of their model that sets it somewhat apart from prior work is the presence of a special reference point, i.e., the status quo. The agenda of social choice in the presence of status quo has recently been pursued by Shapiro, Talmon, and co-authors in a series of papers (Shapiro and Talmon 2018;Shahaf, Shapiro, and Talmon 2019;Bulteau et al 2021;Abramowitz, Shapiro, and Talmon 2021).…”

Section: Related Workmentioning

confidence: 99%

Complexity of Deliberative Coalition Formation

Elkind

Ghosh

Goldberg

2022

AAAI

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Elkind et al. (AAAI'21) introduced a model for deliberative coalition formation, where a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. In their model, agents and proposals are points in a metric space, agents' preferences are determined by distances, and agents deliberate by dynamically forming coalitions around proposals that they prefer over the status quo. The deliberation process operates via k-compromise transitions, where agents from k (current) coalitions come together to form a larger coalition in order to support a (perhaps new) proposal, possibly leaving behind some of the dissenting agents from their old coalitions. A deliberation succeeds if it terminates by identifying a proposal with the largest possible support. For deliberation in d dimensions, Elkind et al. consider two variants of their model: in the Euclidean model, proposals and agent locations are points in R^d and the distance is measured according to ||...||_2; and in the hypercube model, proposals and agent locations are vertices of the d-dimensional hypercube and the metric is the Hamming distance. They show that in the Euclidean model 2-compromises are guaranteed to succeed, but in the hypercube model for deliberation to succeed it may be necessary to use k-compromises with k >= d. We complement their analysis by (1) proving that in both models it is hard to find a proposal with a high degree of support, and even a 2-compromise transition may be hard to compute; (2) showing that a sequence of 2-compromise transitions may be exponentially long; (3) strengthening the lower bound on the size of the compromise for the d-hypercube model from d to 2^Ω(d).

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Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation

Cited by 5 publications

References 42 publications

Byzantine-Robust Decentralized Learning via Self-Centered Clipping

Byzantine-Robust Decentralized Learning via Self-Centered Clipping

Complexity of Deliberative Coalition Formation

Complexity of Deliberative Coalition Formation

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