Fueled by the rapid advances in high-speed mobile networks, live video streaming has seen explosive growth in recent years and many DASH-based bitrate adaptive streaming algorithms were specifically proposed for low-latency video delivery. However, our investigations revealed that these algorithms are susceptible to network condition changes due to the use of solo universal adaptation logics, resulting the playback latency that has substantial variations across highly-fluctuating network environments and fails to meet the service quality requirement all the time. To tackle this challenge, this paper proposes Stateful Live Video Streaming (SLVS), which is a novel learning approach that learns the various network features and optimizes the adaptation logic separately for different network conditions, then dynamically tunes the logic at runtime, so that bitrate decision can better match the changing networks. Extensive evaluations show that SLVS can control playback latency down to 1s while improving Quality-of-Experience (QoE) by 17.7% to 31.8%. Moreover, it has strong robustness to maintain near-second latency over highly-fluctuating networks as well as long-period of video viewing.