Learning to Collaborate in Markov Decision Processes

We consider a two-agent MDP framework where agents repeatedly solve a task in a collaborative setting. We study the problem of designing a learning algorithm for the first agent (A(1)) that facilitates successful collaboration even in cases when the second agent (A(2)) is adapting its policy in an unknown way. The key challenge in our setting is that the first agent faces non-stationarity in rewards and transitions because of the adaptive behavior of the second agent. We design novel online learning algorithms for agent A(1) whose regret decays as O(Tmax{1-3/7.alpha 1/4}), for T learning episodes, provided that the magnitude in the change in agent A(2)'s policy between any two consecutive episodes is upper bounded by O(T-alpha). Here, the parameter a is assumed to be strictly greater than 0, and we show that this assumption is necessary provided that the learning parity with noise problem is computationally hard. We show that sublinear regret of agent A(1) further implies nearoptimality of the agents' joint return for MDPs that manifest the properties of a smooth game.