Strategizing against Q-learners: A Control-theoretical Approach

In this paper, we explore the susceptibility of the independent Q-learning algorithms (a classical and widely used multi-agent reinforcement learning method) to strategic manipulation of sophisticated opponents in normal-form games played repeatedly. We quantify how much strategically sophisticated agents can exploit naive Q-learners if they know the opponents' Q-learning algorithm. To this end, we formulate the strategic actors' interactions as a stochastic game (whose state encompasses Q-function estimates of the Q-learners) as if the Q-learning algorithms are the underlying dynamical system. We also present a quantization-based approximation scheme to tackle the continuum state space and analyze its performance for two competing strategic actors and a single strategic actor both analytically and numerically.