Early detection of cyber-attacks is crucial for a safe and reliable operation of the smart grid. In the literature, outlier detection schemes making sample-by-sample decisions and online detection schemes requiring perfect attack models have been proposed. In this paper, we formulate the online attack anomaly detection problem as a partially observable Markov decision process (POMDP) problem and propose a universal robust online detection algorithm using the framework of model-free reinforcement learning (RL) for POMDPs. Numerical studies illustrate the effectiveness of the proposed RL-based algorithm in timely and accurate detection of cyber-attacks targeting the smart grid.
 We consider reinforcement learning in partially observable domains where the agent can query an expert for demonstrations. Our nonparametric Bayesian approach combines model knowledge, inferred from expert information and independent exploration, with policy knowledge inferred from expert trajectories. We introduce priors that bias the agent towards models with both simple representations and simple policies, resulting in improved policy and model learning. Increasing attention has been paid to reinforcement learning algorithms in recent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of non-Markov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a Monte-Carlo policy evaluation combined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerably better than any deterministic policy. Although the space of stochastic policies is continuous--even for a discrete action space--our algorithm is computationally tractable. Bayesian learning methods have recently been shown to provide an elegant solution to the exploration-exploitation trade-off in reinforcement learning. However most investigations of Bayesian reinforcement learning to date focus on the standard Markov Decision Processes (MDPs). The primary focus of this paper is to extend these ideas to the case of partially observable domains, by introducing the Bayes-Adaptive Partially Observable Markov Decision Processes. This new framework can be used to simultaneously (1) learn a model of the POMDP domain through interaction with the environment, (2) track the state of the system under partial observability, and (3) plan (near-)optimal sequences of actions. An important contribution of this paper is to provide theoretical results showing how the model can be finitely approximated while preserving good learning performance. We present approximate algorithms for belief tracking and planning in this model, as well as empirical results that illustrate how the model estimate and agent's return improve as a function of experience. Recent research on hidden-state reinforcement learning (RL) problems has concentrated on overcoming partial observability by using memory to estimate state. However, such methods are computationally extremely expensive and thus have very limited applicability. This emphasis on state estimation has come about because it has been widely observed that the presence of hidden state or partial observability renders popular RL methods such as Q-learning and Sarsa useless. However, this observation is misleading in two ways: first, the theoretical results supporting it only apply to RL algorithms that do not use eligibility traces, and second these results are worst-case results, which leaves open the possibility that there may be large classes of hidden-state problems in which RL algorithms work well without any state estimation. In this paper we show empirically that Sarsa(λ), a well known family of RL algorithms that use eligibility traces, can work very well on hidden state problems that have good memoryless policies, i.e., on RL problems in which there may well be very poor observability but there also exists a mapping from immediate observations to actions that yields near-optimal return. We apply conventional Sarsa(λ) to four test problems taken from the recent work of Littman, Littman Cassandra and Kaelbling, Parr and Russell, and Chrisman, and in each case we show that it is able to find the best, or a very good, memoryless policy without any of the computational expense of state estimation.  We present a new, model-free reinforcement learning algorithm for learning to control partially-observable Markov decision processes. The algorithm incorporates ideas from action-value based reinforcement learning approaches, such as Q-Learning, as well as ideas from the stochastic optimization literature. Key to our approach is a new definition of action value, which makes the algorithm theoretically sound for partially-observable settings. We show that special cases of our algorithm can achieve probability one convergence to locally optimal policies in the limit, or probably approximately correct hill-climbing to a locally optimal policy in a finite number of samples.