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Grid computing provides a distributed computing environment which supports high performance and data intensive applications by enabling the sharing and selecting various resources. In grid environment resources are heterogeneous and geographically distributed. By receiving a resource request the resource discovery mechanism should return an appropriate resource if there exist one. Resource discovery is a challenging problem because of the heterogeneity and distribution of resources. The centralized and hierarchical resource discovery mechanisms are not suitable for large scale and dynamic resources. On the other hand peer to peer systems are successful in distributed computing because of their scalability and robustness. In this paper, we propose an adaptive peer to peer resource discovery algorithm using reinforcement learning for grid computing that can be used for multi resource requests. The algorithm achieves the most suitable node that can satisfy the requested resource by using the past experience of agents. We compare our model with random walk resource discovery through simulation and the results show that the proposed algorithm provides higher success rate, less message passing and shorter response time. Also the algorithm leads to load balancing in whole grid. According to results our algorithm has a higher performance in large scale grids.