Endogenous evolution of problem difficulty

Develop a version of the problem-solving model in which the difficulty parameter evolves endogenously in response to the solver’s past actions, and determine how such endogenous difficulty dynamics modify optimal exploration policies and learning relative to the baseline with exogenous difficulty.

Background

In the baseline and continuum models, problem difficulty is an exogenous latent state governing the arrival rate of success on valid approaches. The paper’s learning dynamics hinge on how evidence from failures updates beliefs about this exogenous difficulty.

In many applications, actions can change future tractability (e.g., policy implementations that affect future efficacy). Allowing difficulty to evolve endogenously would introduce feedback from actions to the environment, potentially altering belief dynamics and the exploration–exploitation balance.