A feature of the decision theory of perfect equilibrium is that the agent who wants to minimize the optimal loss in the expected time cannot improve his outcome by processing after processing a perfectly balanced forecast. Hu and Wu (FOCS'24) use this to define a quantitative measurement called the measurement decision loss (CDL), which measures the maximum improvement that can be achieved by any post-processing on any relevant loss. Unfortunately, CDL appears to be even less scalable in an offline setting, given the black-box access to predictions and labels. We propose to circumvent this by restricting attention to structured families of post-processing functions K. We describe the relative loss of measurement decision Kmarked CDLK where we consider all relevant losses but limit post-processing to a structured family K. We develop a comprehensive theory of when CDLK information is theoretical and computable, and used to prove both the upper and lower bounds of natural classes. K. In addition to introducing new definitions and algorithmic approaches to the estimation theory of decision making, our results provide strong justifications for some widely used re-estimation procedures in machine learning.
- † University of Texas at Austin
- ‡ Harvard University
