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--- | ||
title: Multi-Agent Bandit Learning through Heterogeneous Action Erasure Channels | ||
software: https://github.com/mervekarakas/mamab_erasures | ||
abstract: Multi-Armed Bandit (MAB) systems are witnessing an upswing in applications | ||
within multi-agent distributed environments, leading to the advancement of collaborative | ||
MAB algorithms. In such settings, communication between agents executing actions | ||
and the primary learner making decisions can hinder the learning process. A prevalent | ||
challenge in distributed learning is action erasure, often induced by communication | ||
delays and/or channel noise. This results in agents possibly not receiving the intended | ||
action from the learner, subsequently leading to misguided feedback. In this paper, | ||
we introduce novel algorithms that enable learners to interact concurrently with | ||
distributed agents across heterogeneous action erasure channels with different action | ||
erasure probabilities. We illustrate that, in contrast to existing bandit algorithms, | ||
which experience linear regret, our algorithms assure sub-linear regret guarantees. | ||
Our proposed solutions are founded on a meticulously crafted repetition protocol | ||
and scheduling of learning across heterogeneous channels. To our knowledge, these | ||
are the first algorithms capable of effectively learning through heterogeneous action | ||
erasure channels. We substantiate the superior performance of our algorithm through | ||
numerical experiments, emphasizing their practical significance in addressing issues | ||
related to communication constraints and delays in multi-agent environments. | ||
layout: inproceedings | ||
series: Proceedings of Machine Learning Research | ||
publisher: PMLR | ||
issn: 2640-3498 | ||
id: a-hanna24a | ||
month: 0 | ||
tex_title: Multi-Agent Bandit Learning through Heterogeneous Action Erasure Channels | ||
firstpage: 3898 | ||
lastpage: 3906 | ||
page: 3898-3906 | ||
order: 3898 | ||
cycles: false | ||
bibtex_author: A Hanna, Osama and Karakas, Merve and Yang, Lin and Fragouli, Christina | ||
author: | ||
- given: Osama | ||
family: A Hanna | ||
- given: Merve | ||
family: Karakas | ||
- given: Lin | ||
family: Yang | ||
- given: Christina | ||
family: Fragouli | ||
date: 2024-04-18 | ||
address: | ||
container-title: Proceedings of The 27th International Conference on Artificial Intelligence | ||
and Statistics | ||
volume: '238' | ||
genre: inproceedings | ||
issued: | ||
date-parts: | ||
- 2024 | ||
- 4 | ||
- 18 | ||
pdf: https://proceedings.mlr.press/v238/a-hanna24a/a-hanna24a.pdf | ||
extras: [] | ||
# Format based on Martin Fenner's citeproc: https://blog.front-matter.io/posts/citeproc-yaml-for-bibliographies/ | ||
--- |
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--- | ||
title: 'Lexicographic Optimization: Algorithms and Stability' | ||
abstract: 'A lexicographic maximum of a set $X \subseteq R^n$ is a vector in $X$ whose | ||
smallest component is as large as possible, and subject to that requirement, whose | ||
second smallest component is as large as possible, and so on for the third smallest | ||
component, etc. Lexicographic maximization has numerous practical and theoretical | ||
applications, including fair resource allocation, analyzing the implicit regularization | ||
of learning algorithms, and characterizing refinements of game-theoretic equilibria. | ||
We prove that a minimizer in $X$ of the exponential loss function $L_c(x) = \sum_i | ||
\exp(-c x_i)$ converges to a lexicographic maximum of $X$ as $c \to \infty$, provided | ||
that $X$ is \emph{stable} in the sense that a well-known iterative method for finding | ||
a lexicographic maximum of $X$ cannot be made to fail simply by reducing the required | ||
quality of each iterate by an arbitrarily tiny degree. Our result holds for both | ||
near and exact minimizers of the exponential loss, while earlier convergence results | ||
made much stronger assumptions about the set $X$ and only held for the exact minimizer. | ||
We are aware of no previous results showing a connection between the iterative method | ||
for computing a lexicographic maximum and exponential loss minimization. We show | ||
that every convex polytope is stable, but that there exist compact, convex sets | ||
that are not stable. We also provide the first analysis of the convergence rate | ||
of an exponential loss minimizer (near or exact) and discover a curious dichotomy: | ||
While the two smallest components of the vector converge to the lexicographically | ||
maximum values very quickly (at roughly the rate $\frac{\log n}{c}$), all other | ||
components can converge arbitrarily slowly.' | ||
layout: inproceedings | ||
series: Proceedings of Machine Learning Research | ||
publisher: PMLR | ||
issn: 2640-3498 | ||
id: abernethy24a | ||
month: 0 | ||
tex_title: 'Lexicographic Optimization: Algorithms and Stability' | ||
firstpage: 2503 | ||
lastpage: 2511 | ||
page: 2503-2511 | ||
order: 2503 | ||
cycles: false | ||
bibtex_author: Abernethy, Jacob A. and Schapire, Robert and Syed, Umar | ||
author: | ||
- given: Jacob A. | ||
family: Abernethy | ||
- given: Robert | ||
family: Schapire | ||
- given: Umar | ||
family: Syed | ||
date: 2024-04-18 | ||
address: | ||
container-title: Proceedings of The 27th International Conference on Artificial Intelligence | ||
and Statistics | ||
volume: '238' | ||
genre: inproceedings | ||
issued: | ||
date-parts: | ||
- 2024 | ||
- 4 | ||
- 18 | ||
pdf: https://proceedings.mlr.press/v238/abernethy24a/abernethy24a.pdf | ||
extras: [] | ||
# Format based on Martin Fenner's citeproc: https://blog.front-matter.io/posts/citeproc-yaml-for-bibliographies/ | ||
--- |
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