We consider metrical task systems on general metric spaces with $n$ points, and show that any fully randomized algorithm can be turned into a randomized algorithm that uses only $2\log n$ random bits, and achieves the same competitive ratio up to a factor $2$. This provides the first order-optimal barely random algorithms for metrical task systems, i.e. which use a number of random bits that does not depend on the number of requests addressed to the system. We put forward an equivalent view that we call collective metrical task systems where $k$ agents in a metrical task system team up, and suffer the average cost paid by each agent. Our results imply that such team can be $O(\log n^2)$-competitive, as soon as $k\geq n^2$ (in comparison, a single agent is $\Omega(n)$-competitive at best). We discuss implications on various aspects of online decision making such as: distributed systems, transaction costs, and advice complexity, suggesting broad applicability.

翻译：我们考虑一般度量空间上具有$n$个点的度量任务系统，证明了任意完全随机算法均可转化为仅使用$2\log n$个随机比特的随机算法，且其竞争比在因子$2$范围内保持不变。这为度量任务系统首次提供了具有阶最优性的几乎随机算法——即算法使用的随机比特数与系统处理的请求数量无关。我们提出一种等价的视角，称为集体度量任务系统：其中$k$个智能体在度量任务系统中协同工作，共同承担每个智能体支付的平均成本。我们的结果表明，只要$k \geq n^2$，该团队即可达到$O(\log n^2)$-竞争比（相比之下，单个智能体至多达到$\Omega(n)$-竞争比）。本文进一步讨论了该方法在在线决策各领域（如分布式系统、交易成本及建议复杂性）的潜在应用，彰显其广泛的适用性。