  In this paper, we are interested in systems with multiple agents that wish to
collaborate in order to accomplish a common task while a) agents have different
information (decentralized information) and b) agents do not know the model of
the system completely i.e., they may know the model partially or may not know
it at all. The agents must learn the optimal strategies by interacting with
their environment i.e., by decentralized Reinforcement Learning (RL). The
presence of multiple agents with different information makes decentralized
reinforcement learning conceptually more difficult than centralized
reinforcement learning. In this paper, we develop a decentralized reinforcement
learning algorithm that learns $\epsilon$-team-optimal solution for partial
history sharing information structure, which encompasses a large class of
decentralized control systems including delayed sharing, control sharing, mean
field sharing, etc. Our approach consists of two main steps. In the first step,
we convert the decentralized control system to an equivalent centralized POMDP
(Partially Observable Markov Decision Process) using an existing approach
called common information approach. However, the resultant POMDP requires the
complete knowledge of system model. To circumvent this requirement, in the
second step, we introduce a new concept called "Incrementally Expanding
Representation" using which we construct a finite-state RL algorithm whose
approximation error converges to zero exponentially fast. We illustrate the
proposed approach and verify it numerically by obtaining a decentralized
Q-learning algorithm for two-user Multi Access Broadcast Channel (MABC) which
is a benchmark example for decentralized control systems.
