This paper proposes a novel fast online methodology for outlier detection called the exception maximization outlier detection method(EMODM), which employs probabilistic models and statistical algorithms to detect abnormal patterns from the outputs of complex systems. The EMODM is based on a two-state Gaussian mixture model and demonstrates strong performance in probability anomaly detection working on real-time raw data rather than using special prior distribution information. We confirm this using the synthetic data from two numerical cases. For the real-world data, we have detected the short circuit pattern of the circuit system using EMODM by the current and voltage output of a three-phase inverter. The EMODM also found an abnormal period due to COVID-19 in the insured unemployment data of 53 regions in the United States from 2000 to 2024. The application of EMODM to these two real-life datasets demonstrated the effectiveness and accuracy of our algorithm.

Decentralized learning has shown great promise for cooperative multi-agent reinforcement learning (MARL). However, non-stationarity remains a significant challenge in fully decentralized learning. In the paper, we tackle the non-stationarity problem in the simplest and fundamental way and propose multi-agent alternate Q-learning (MA2QL), where agents take turns updating their Q-functions by Q-learning. MA2QL is a minimalist approach to fully decentralized cooperative MARL but is theoretically grounded. We prove that when each agent guarantees $\varepsilon$-convergence at each turn, their joint policy converges to a Nash equilibrium. In practice, MA2QL only requires minimal changes to independent Q-learning (IQL). We empirically evaluate MA2QL on a variety of cooperative multi-agent tasks. Results show MA2QL consistently outperforms IQL, which verifies the effectiveness of MA2QL, despite such minimal changes.