We consider a twoagent 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 (A1) that facilitates a successful collaboration even in cases when the second agent (A2) is adapting its policy in an unknown way. The key challenge in our setting is that the presence of the second agent leads to nonstationarity and nonobliviousness of rewards and transitions for the first agent.
We design novel online learning algorithms for agent A1 whose regret decays as $O(T^{1\frac{3}{7} \cdot \alpha})$ with $T$ learning episodes provided that the magnitude of agent A2's policy changes between any two consecutive episodes are upper bounded by $O(T^{\alpha})$. Here, the parameter $\alpha$ is assumed to be strictly greater than $0$, and we show that this assumption is necessary provided that the {\em learning parity with noise} problem is computationally hard. We show that sublinear regret of agent A1 further implies nearoptimality of the agents' joint return for MDPs that manifest the properties of a {\em smooth} game.
Author Information
Goran Radanovic (Harvard University)
Rati Devidze (Max Planck Institute for Software Systems)
David Parkes (Harvard University)
Adish Singla (Max Planck Institute (MPISWS))
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