AI 中文总结
该研究开发在线算法，利用公平硬币翻转熵源对离散随机变量序列抽样，针对概率分布序列生成输出，期望用较少硬币翻转和少量持久空间，通过改进采样方案实现渐近最优空间，推广了随机性回收方法。
AI 中文摘要
我们开发了一种高效的在线算法，用于在实值概率由有理近似表示的标准实计算模型中，使用独立同分布的公平硬币翻转的熵源对离散随机变量序列进行抽样。对于任何概率分布序列\(F_1,F_2,\dots\)，我们的采样器生成\(n\)个输出\(X_1\sim F_1,\dots,X_n\sim F_n\)，期望使用至多\(\mathbb{E}[H(F_1)+\dots + H(F_n)] + O(\log n)\)次硬币翻转，同时占用\(O(\log n)\)位的持久空间，其中\(H\)是香农熵。在标准假设下，我们证明了我们的采样器用于实现这种信息理论上最优熵率的空间是渐近最优的。关键思想是用局部离散均匀状态代替Han和Hoshi（1997）的全局算术解码采样方案，在给定熵损失的情况下使空间呈指数减少。我们的方法适用于具有无理概率和可数无限支持的分布，将最近的随机性回收方法推广到分母有界的有限有理分布之外。
英文摘要
We develop an efficient online algorithm to sample a sequence of discrete random variables using an entropy source of i.i.d. fair coin flips, in a standard model of real computation where real-valued probabilities are represented by rational approximations. For any sequence $F_1, F_2, \dots$ of probability distributions, our sampler generates $n$ outputs $X_1 \sim F_1, \dots, X_n \sim F_n$ using at most $\mathbb{E}\left[H(F_1) +\dots + H(F_n)\right] + O(\log n)$ coin flips in expectation while carrying $O(\log n)$ bits of persistent space, where $H$ is the Shannon entropy. Under standard assumptions, we prove that the space used by our sampler to achieve this information-theoretically optimal entropy rate is asymptotically optimal. The key idea is to replace the global arithmetic-decoding sampling scheme of Han and Hoshi (1997) with a local discrete uniform state, yielding an exponential reduction in space for a given entropy loss. Our approach applies to distributions with irrational probabilities and countably infinite supports, generalizing recent randomness-recycling methods beyond finite rational distributions with bounded denominator.
