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 discuss implications on various aspects of online decision-making such as: distributed systems, advice complexity, and transaction costs, suggesting broad applicability. 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 a team can be $O(\log^2 n)$-competitive as soon as $k\geq n^2$. In comparison, a single agent is always $\Omega(n)$-competitive.

翻译：我们研究了定义在具有 $n$ 个点的一般度量空间上的度量任务系统，并证明了任何完全随机化算法都可以转化为仅使用 $2\log n$ 个随机比特的随机化算法，且其竞争比与原算法相比最多只差 $2$ 倍。这为度量任务系统提供了首个阶数最优的几乎随机算法，即所使用的随机比特数不依赖于系统处理的请求数量。我们讨论了这一结果对在线决策各方面的影响，例如：分布式系统、建议复杂性和交易成本，表明了其广泛的适用性。我们提出了一种等价的视角，称之为集体度量任务系统，其中度量任务系统中的 $k$ 个智能体组成团队，并承担每个智能体所支付的平均成本。我们的结果表明，只要 $k \geq n^2$，这样一个团队就可以达到 $O(\log^2 n)$ 的竞争比。相比之下，单个智能体的竞争比总是 $\Omega(n)$。