This paper reports applications of Difference of Convex functions (DC) programming to Learning from Demonstrations (LfD) and Reinforcement Learning (RL) with expert data. This is made possible because the norm of the Optimal Bellman Residual (OBR), which is at the heart of many RL and LfD algorithms, is DC. Improvement in performance is demonstrated on two specific algorithms, namely Reward-regularized Classification for Apprenticeship Learning (RCAL) and Reinforcement Learning with Expert Demonstrations (RLED), through experiments on generic Markov Decision Processes (MDP), called Garnets.

Large Markov Decision Processes (MDPs) are usually solved using Approximate Dynamic Programming (ADP) methods such as Approximate Value Iteration (AVI) or Approximate Policy Iteration (API). The main contribution of this paper is to show that, alternatively, the optimal state-action value function can be estimated using Difference of Convex functions (DC) Programming. To do so, we study the minimization of a norm of the Optimal Bellman Residual (OBR) $T^*Q-Q$, where $T^*$ is the so-called optimal Bellman operator. Controlling this residual allows controlling the distance to the optimal action-value function, and we show that minimizing an empirical norm of the OBR is consistant in the Vapnik sense. Finally, we frame this optimization problem as a DC program. That allows envisioning using the large related literature on DC Programming to address the Reinforcement Leaning (RL) problem.

This paper adresses the inverse reinforcement learning (IRL) problem, that is inferring a reward for which a demonstrated expert behavior is optimal. We introduce a new algorithm, SCIRL, whose principle is to use the so-called feature expectation of the expert as the parameterization of the score function of a multi-class classifier. This approach produces a reward function for which the expert policy is provably near-optimal. Contrary to most of existing IRL algorithms, SCIRL does not require solving the direct RL problem. Moreover, with an appropriate heuristic, it can succeed with only trajectories sampled according to the expert behavior. This is illustrated on a car driving simulator.