Non-volatile memory express (NVMe) solid-state drives (SSDs) have been widely adopted in multi-tenant cloud computing environments or multi-programming systems. The on-board DRAM cache inside NVMe SSDs can efficiently reduce the disk accesses and extend the lifetime of SSDs. Current SSD cache management research either improves cache hit ratio while ignoring fairness, or improves fairness while sacrificing overall performance. In this paper, we present MLCache, a space-efficient shared cache management scheme for NVMe SSDs. By learning the impact of reuse distance on cache allocation, a workload-generic neural network model is built. At runtime, MLCache continuously monitors the reuse distance distribution for the neural network module to obtain space-efficient allocation decisions. MLCache also proposes an efficient parallel writing back strategy based on hit ratio and response time, to improve fairness. Experimental results show MLCache improves the write hit ratio when compared to baseline, and MLCache strongly safeguards the fairness of SSDs with parallel write-back and maintains a low level of degradation.