Intelligent reflecting surface (IRS) is a revolutionizing technology for improving the spectral and energy efficiency of future wireless networks. In this paper, we consider a downlink large-scale system empowered by multi-IRS to aid communication between the multiple base stations (BSs) and multiple user equipment (UEs). We target maximizing the sum rate by jointly optimizing the UE association, the transmit powers of BSs, and the configurations of the IRS beamforming. Due to the applicability restrictions of conventional optimization methods and their high complexity with large-scale networks in dynamic environments, deep reinforcement (DRL) learning is adopted as an alternative approach to finding optimal solutions. First, we model the optimization problem as a multi-agent Markov decision problem (MAMDP). Then, because large-scale wireless networks are naturally complex and changeable, and because many entities interact and affect how the whole system works, it is important to use a multi-agent approach to understand the complex dependencies and relationships between the different parts. In order to solve the problem, we propose a cooperative multi-agent deep reinforcement learning (MADRL)-based algorithm that works for both continuous and discrete IRS phase shifts. Simulation results validate that the proposed algorithm surpasses iterative optimization benchmarks regarding both sum rate performance and convergence.