This paper deals with the problem of soft guessing under log-loss distortion (logarithmic loss) that was recently investigated by [Wu and Joudeh, IEEE ISIT, pp. 466--471, 2023]. We extend this problem to soft guessing allowing errors, i.e., at each step, a guesser decides whether to stop the guess or not with some probability and if the guesser stops guessing, then the guesser declares an error. We show that the minimal expected value of the cost of guessing under the constraint of the error probability is characterized by the smooth R\'enyi entropy. Furthermore, we carry out an asymptotic analysis for a stationary and memoryless source.

翻译：本文研究了近期由[Wu and Joudeh, IEEE ISIT, pp. 466--471, 2023]探讨的对数损失失真（对数损失）下的软猜测问题。我们将此问题扩展至允许错误的软猜测场景，即每一步中，猜测者以一定概率决定是否停止猜测，若停止猜测则声明错误。我们证明：在错误概率约束下，猜测成本的最小期望值由平滑Rényi熵刻画。此外，我们对平稳无记忆信源进行了渐近分析。