Extending two-part epiplexity results to generalized (regret-based) epiplexity

Determine whether the theoretical results established for two-part epiplexity (based on time-bounded MDL with an explicit model-and-data code) extend to the generalized, regret-based notion of epiplexity defined via prequential and other one-part codes. Specifically, develop formal analogues of the two-part epiplexity theorems under the generalized definition or provide counterexamples demonstrating where such analogues fail.

Background

Beyond the two-part MDL formulation used to define epiplexity, the authors discuss a generalized, regret-based view that applies to one-part codes (e.g., prequential). This generalized perspective can be more practical for modern learning systems but lacks the direct theoretical transfer from the two-part setting.

The paper’s core results—such as separations related to deterministic transformations, factorization dependence, and the characterization of structural versus random content under computational constraints—are proved for the two-part epiplexity. Whether analogous guarantees hold under generalized (regret-based) epiplexity remains explicitly unresolved, and addressing this would clarify the robustness of the framework across coding schemes.