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新论文 · v1arXiv:2611.09806

分布式多臂老虎机的一种高效同步方案

An Efficient Synchronization Scheme for Distributed Bandits

Raymond Zhang, Henrique Miyamoto, Richard Combes, Sheng Yang

AI 速读 基于摘要

该论文将分布式多臂老虎机中两名玩家的同步问题建模为通信问题，用随机编码集合与最大似然解码分析同步错误指数，并提出达到相同错误指数的通用解码器，进而给出同步方案的遗憾上界。

cs.IT

arXiv ↗PDF ↗
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We study the problem of synchronizing two players in a \emph{distributed multi-armed bandit} setting. The probability of \emph{synchronization error} is analyzed by recasting synchronization as a \emph{communication problem}. Using a well-designed random coding ensemble, we derive error exponents for the maximum-likelihood decoder. We then introduce a \emph{universal decoder} that achieves the same error exponents as the optimal decoder. Finally, applying these results to distributed multi-armed bandits, we show an upper bound on the regret of our synchronization scheme.

版本更新 · v2arXiv:2502.17175

Linear Bandits on Ellipsoids: Minimax Optimal Algorithms

Raymond Zhang, Hedi Hadiji, Richard Combes

原文摘要

We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm, which must be at least $Ω(\min(d σ\sqrt{T} + d \|θ\|_{A}, \|θ\|_{A} T))$ where $d$ is the dimension, $T$ the time horizon, $σ^2$ the noise variance, $A$ a matrix defining the set of actions and $θ$ the vector of unknown parameters. We then provide an algorithm whose regret matches this bound to a multiplicative universal constant. The algorithm is non-classical in the sense that it is not optimistic, and it is not a sampling algorithm. The main idea is to combine a novel sequential procedure to estimate $\|θ\|$, followed by an explore-and-commit strategy informed by this estimate. The algorithm is highly computationally efficient, and a run requires only time $O(dT + d^2 \log(T/d) + d^3)$ and memory $O(d^2)$, in contrast with known optimistic algorithms, which are not implementable in polynomial time. We go beyond minimax optimality and show that our algorithm is locally asymptotically minimax optimal, a much stronger notion of optimality. We further provide numerical experiments to illustrate our theoretical findings.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.09466

Symmetry Breaking over Multiway Channels

Raymond Zhang, Richard Combes, Sheng Yang

原文摘要

Identical users running the same algorithm must often break their symmetry and agree on distinct roles, as in leader election, naming, and resource allocation. We study anonymous symmetry breaking over a discrete memoryless multiway channel invariant under permutations of its $J$ users: each user observes only a private output and must choose a number in $\{1,\dots,J\}$, and the symmetry is broken if the $J$ numbers are distinct. Using a Rényi change of measure, we derive a finite-blocklength converse on the error probability of every symmetric causal protocol, including adaptive and randomized ones. For achievability, block coding with random names reduces the problem to all-source multicast, for which we derive a Gallager random-coding exponent for every fixed $J$, and a cut-set bound that limits the exponent of the probability that two names coincide or are decoded wrongly. Interactive role controllers instead let the users contend for identifiers directly: we give their exact error probability, an achievable exponent given by a spectral radius when some outputs certify a role, and a floor for finite-state controllers when every output has positive probability, and we introduce generalized musical chairs. On a noisy bandit channel motivated by multiplayer multi-armed bandits, with noiseless collisions and arms of a common mean below one, interactive schemes provably exceed the limit of name decoding, and numerical estimates suggest the same with noisy collisions. For two users, noiseless collisions, one informative arm and a silent arm, the optimal error probability is determined up to a factor of two.

cs.IT

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arXiv ↗PDF ↗