Quantification of transfer in reinforcement learning via regret bounds for learning agents

We present an approach for the quantification of the usefulness of transfer in reinforcement learning via regret bounds for a multi-agent setting. Considering a number of $$\varvec{\aleph }$$ agents operating in the same Markov decision process, however possibly with different reward functions, we consider the regret each agent suffers with respect to an optimal policy maximizing its average reward. We show that when the agents share their observations the mutual regret of all agents is smaller by a factor of $$\varvec{\sqrt{\aleph }}$$ compared to the case when each agent has to rely on the information collected by itself. This result demonstrates how considering the regret in multi-agent settings can provide theoretical bounds on the benefit of sharing observations in transfer learning.