Apprenticeship Learning via Frank-Wolfe

We consider the applications of the Frank-Wolfe (FW) algorithm for Apprenticeship Learning (AL). In this setting, there is a Markov Decision Process (MDP), but the reward function is not given explicitly. Instead, there is an expert that acts according to some policy, and the goal is to find a policy whose feature expectations are closest to those of the expert policy. We formulate this problem as finding the projection of the feature expectations of the expert on the feature expectations polytope -- the convex hull of the feature expectations of all the deterministic policies in the MDP. We show that this formulation is equivalent to the AL objective and that solving this problem using the FW algorithm is equivalent to the most known AL algorithm, the projection method of Abbeel and Ng (2004). This insight allows us to analyze AL with tools from the convex optimization literature and to derive tighter bounds on AL. Specifically, we show that a variation of the FW method that is based on taking ``away steps" achieves a linear rate of convergence when applied to AL. We also show experimentally that this version outperforms the FW baseline. To the best of our knowledge, this is the first work that shows linear convergence rates for AL.

• Machine Intelligence