## Abstract

We consider a multi-agent episodic MDP setup where an agent (leader) takes action at each step of the episode followed by another agent (follower). The state evolution and rewards depend on the joint action pair of the leader and the follower. Such types of interactions can find applications in many domains such as smart grids, mechanism design, security, and policymaking. We are interested in how to learn policies for both the players with provable performance guarantee under a bandit feedback setting. We focus on a setup where both the leader and followers are non-myopic, i.e., they both seek to maximize their rewards over the entire episode and consider a linear MDP which can model continuous state-space which is very common in many RL applications. We propose a model-free RL algorithm and show that Õ(√d^{3}H^{3}T) regret bounds can be achieved for both the leader and the follower, where d is the dimension of the feature mapping, H is the length of the episode, and T is the total number of steps under the bandit feedback information setup. Thus, our result holds even when the number of states becomes infinite. The algorithm relies on novel adaptation of the single agent LSVI-UCB algorithm. Specifically, we replace the standard greedy policy (as the best response) with the soft-max policy for both the leader and the follower. This turns out to be key in establishing uniform concentration bound for the value functions. To the best of our knowledge, this is the first sub-linear regret bound guarantee for the Markov games with non-myopic followers with function approximation.

Original language | English (US) |
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Pages (from-to) | 1112-1124 |

Number of pages | 13 |

Journal | Proceedings of Machine Learning Research |

Volume | 211 |

State | Published - 2023 |

Externally published | Yes |

Event | 5th Annual Conference on Learning for Dynamics and Control, L4DC 2023 - Philadelphia, United States Duration: Jun 15 2023 → Jun 16 2023 |

## All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability