00364 Œ1028436a8132748621c0d2ba2ba130

368

Obenchain

1

FigurÄ™ 4. Logistic Regret

where the K's are again positive constants.

In both the logistic and inverted normal cases, regret is zero only at the target, X = T; regret approaches a maximum of K in the limit as X approaches ±infinity; and regret eÄ…uals K/2 at X = T±H. Thus the H parameter of [4] and [5] sets the scalÄ™ along the X-axis. Spiring (1993) expresses [5] in a morÄ™ familiar form as a power of e = 2.71828...; here, we use