Detecting anomalies in large-scale system logs is critical for the reliability and security of modern computing infrastructure. We present LogNEO, a log anomaly detector built on EleutherAI's GPT-Neo (1.3B parameters) and fine-tuned with a novel partial-credit, exponentially decaying position-aware reward scheme combined with cross-entropy regularisation via Proximal Policy Optimisation (PPO). The position-aware reward explicitly models prediction difficulty: early positions receive higher rewards for correct predictions, while later positions incur stronger penalties for errors. LogNEO attains F1-scores of 0.927, 0.913, and 0.984 on the HDFS, BGL, and Thunderbird benchmarks, improving recall by up to 6 percentage points over the prior state-of-the-art LogGPT while maintaining comparable precision. A production microservice deployment over Apache Kafka, Redis, and TensorRT-accelerated inference demonstrates 45 ms end-to-end latency at 15,000 events per second.