  Multi-agent reinforcement learning involves multiple agents interacting with
each other and a shared environment to complete tasks. When rewards provided by
the environment are sparse, agents may not receive immediate feedback on the
quality of actions that they take, thereby affecting learning of policies. In
this paper, we propose a method called Shaping Advice in deep Multi-agent
reinforcement learning (SAM) to augment the reward signal from the environment
with an additional reward termed shaping advice. The shaping advice is given by
a difference of potential functions at consecutive time-steps. Each potential
function is a function of observations and actions of the agents. The shaping
advice needs to be specified only once at the start of training, and can be
easily provided by non-experts. We show through theoretical analyses and
experimental validation that shaping advice provided by SAM does not distract
agents from completing tasks specified by the environment reward.
Theoretically, we prove that convergence of policy gradients and value
functions when using SAM implies convergence of these quantities in the absence
of SAM. Experimentally, we evaluate SAM on three tasks in the multi-agent
Particle World environment that have sparse rewards. We observe that using SAM
results in agents learning policies to complete tasks faster, and obtain higher
rewards than: i) using sparse rewards alone; ii) a state-of-the-art reward
redistribution method.
