title: Occupy & Specify: Investigations into a Maximum Credit Assignment Occupancy Objective for Data-efficient Reinforcement Learning
abstract: The capability to widely sample the state and action spaces is a key ingredient toward building effective reinforcement learning algorithms. The trade-off between exploration and exploitation generally requires the use of a data model, from which novelty bonuses are estimated and used to bias the return toward wider exploration. Surprisingly, little is known about the optimization objective followed when novelty (or entropy) bonuses are considered. Following the ``probability matching'' principle, we interpret here returns (cumulative rewards) as set points that fixate the occupancy of the state space, that is the frequency at which the different states are expected to be visited during trials. The circular dependence of the rewards sampling on the occupancy/policy makes it difficult to evaluate. We provide here a variational formulation for the matching objective, named MaCAO (Maximal Credit Assignment Occupancy) that interprets rewards as a log-likelihood on occupancy, that operates anticausally from the effects toward the causes. It is, broadly speaking, an estimation of the contribution of a state toward reaching a (future) goal. It is constructed so as to provide better convergence guaranties, with a complementary term serving as a regularizer, that, in principle, may reduce the greediness. In the absence of an explicit target occupancy, a uniform prior is used, making the regularizer consistent with a MaxEnt (Maximum Entropy) objective on states. Optimizing the entropy on states in known to be more tricky than optimizing the entropy on actions, because of an external sampling through the (unknown) environment, that prevents the propagation of a gradient. In our practical implementations, the MaxEnt regularizer is interpreted as a TD-error rather than a reward, making it possible to define an update in both the discrete and continuous cases. It is implemented on an actor-critic off-policy setup with a replay buffer, using gradient descent on a multi-layered neural network, and shown to provide significant increase in the sampling efficacy, that reflects in a reduced training time and higher returns on a set of classical motor learning benchmarks, in both the dense and the sparse rewards cases. 
authors: Emmanuel Daucé
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