Weakly Coupled Deep Q-Networks
Ibrahim El Shar Daniel R. Jiang
We propose weakly coupled deep Q-networks (WCDQN), a novel deep reinforcement
learning algorithm that enhances performance in a class of structured problems
called weakly coupled Markov decision processes (WCMDP). WCMDPs consist of
multiple independent subproblems connected by an action space constraint, which
is a structural property that frequently emerges in practice. Despite this
appealing structure, WCMDPs quickly become intractable as the number of
subproblems grows. WCDQN employs a single network to train multiple DQN
"subagents", one for each subproblem, and then combine their solutions to
establish an upper bound on the optimal action value. This guides the main DQN
agent towards optimality. We show that the tabular version, weakly coupled
Q-learning (WCQL), converges almost surely to the optimal action value.
Numerical experiments show faster convergence compared to DQN and related
techniques in settings with as many as 10 subproblems, $3^{10}$ total actions,
and a continuous state space.