Improved Bounds on the Moments of Guessing Cost

Guessing a random variable with finite or countably infinite support in which each selection leads to a positive cost value has recently been studied within the context of "guessing cost". In those studies, similar to standard guesswork, upper and lower bounds for the ρ-th moment of guessing cost are described in terms of the known measure Rényi’s entropy. In this study, we non-trivially improve the known bounds using previous techniques along with new notions such as balancing cost. We have demonstrated that the novel lower bound proposed in this work, achieves 5.84%, 18.47% higher values than that of the known lower bound for ρ = 1 and ρ = 5, respectively. As for the upper bound, the novel expression provides 10.93%, 5.54% lower values than that of the previously presented bounds for ρ = 1 and ρ = 5, respectively.