  Many transfer problems require re-using previously optimal decisions for
solving new tasks, which suggests the need for learning algorithms that can
modify the mechanisms for choosing certain actions independently of those for
choosing others. However, there is currently no formalism nor theory for how to
achieve this kind of modular credit assignment. To answer this question, we
define modular credit assignment as a constraint on minimizing the algorithmic
mutual information among feedback signals for different decisions. We introduce
what we call the modularity criterion for testing whether a learning algorithm
satisfies this constraint by performing causal analysis on the algorithm
itself. We generalize the recently proposed societal decision-making framework
as a more granular formalism than the Markov decision process to prove that for
decision sequences that do not contain cycles, certain single-step temporal
difference action-value methods meet this criterion while all policy-gradient
methods do not. Empirical evidence suggests that such action-value methods are
more sample efficient than policy-gradient methods on transfer problems that
require only sparse changes to a sequence of previously optimal decisions.
