Abstract. The traditional agenda in Multiagent Learning (MAL) has been to develop learners that guarantee convergence to an equilibrium in self-play or that converge to playing the best response against an opponent using one of a fixed set of known targeted strategies. This paper introduces an algorithm called Learn or Exploit for Adversary Induced Markov Decision Process (LoE-AIM) that targets optimality against any learning opponent that can be treated as a memory bounded adversary. LoE-AIM makes no prior assumptions about the opponent and is tailored to optimally exploit any adversary which induces a Markov decision process in the state space of joint histories. LoE-AIM either explores and gathers new information about the opponent or converges to the best response to the partially learned opponent strategy in repeated play. We further extend LoE-AIM to account for online repeated interactions against the same adversary with plays against other adversaries interleaved in between. LoE-AIM-repeated stores learned knowledge about an adversary, identifies the adversary in case of repeated interaction, and reuses the stored knowledge about the behavior of the adversary to enhance learning in the current epoch of play. LoE-AIM and LoE-AIM-repeated are fully implemented, with results demonstrating their superiority over other existing MAL algorithms. 1

Planning how to interact against bounded memory and unbounded memory learning opponents needs different treatment. Thus far, however, work in this area has shown how to design plans against bounded memory learning opponents, but no work has dealt with the unbounded memory case. This paper tackles this gap. In particular, we frame thisas a planning problem using the framework of repeated matrix games, where the planner’s objective is to compute the best exploiting sequence of actions against a learning opponent. The particular class of opponent we study uses a fictitious play process to update her beliefs, but the analysis generalizes to many forms of Bayesian learning agents. Our analysis is inspired by Banerjee and Peng’s AIM framework, which works for planning and learning against bounded memory opponents (e.g an adaptive player). Building on this, we show how an unbounded memory opponent (specifically a fictitious player) can also be modelled as a finite MDP and present a new efficient algorithm that can find a way to exploit the opponent by computing in polynomial time a sequence of play that can obtain a higher average reward than those obtained by playing a game theoretic (Nash or correlated) equilibrium.

In this paper we study, for the first time explicitly, the implications of endowing an interested party (i.e. a teacher) with the ability to modify the underlying dynamics of the environment, in order to encourage an agent to learn to follow a specific policy. We introduce a cost function which can be used by the teacher to balance the modifications it makes to the underlying environment dynamics, with the learner’s performance compared to some ideal, desired, policy. We formulate teacher’s problem of determining optimal environment changes as a planning and control problem, and empirically validate the effectiveness of our model.