Re-configurable intelligent surface (RIS)-aided communication has been envisaged as a frontier scheme to enable ultra-high spectral efficiency (SE) and energy efficiency (EE) for next-generation communication. This paper investigates an unconventional framework of RIS-aided full-duplex (FD) multi-user multiple-input multiple-output (MIMO) communication and analyzes its resource efficiency (RE), a preferable performance metric for realizing trade-off between SE and EE maximization. In particular, we focus on the RE maximization problem via a joint optimization of transmit covariance, optimal receive covariance, and phase-shift matrices for each RIS subject to the given constraint on the power budget. To solve the formulated non-convex problem, we propose two optimization approaches: a) policy gradient-based deep-reinforcement learning (DRL) algorithm based on a Markov decision process formulation for a stochastic-time varying channel and b) alternate optimization (AO) algorithm based on general approximations and majorization-minimization (MM) for static channel conditions. Simulation results validate the out-performance of the considered RIS-aided FD-MIMO system compared to the counterpart system with half-duplex (HD) mode and without RIS case. The proposed DRL algorithm achieves comparable RE performance with reduced computational complexity and running time compared to the traditional AO-based algorithm.