Average optimality for continuous-time Markov decision processes in polish spaces

This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying continuous-time jump Markov processes are allowed to be unbounded, and the reward rates may have neither upper nor lower bounds. We first provide two optimality inequalities with opposed directions, and also give suitable conditions under which the existence of solutions to the two optimality inequalities is ensured. Then, from the two optimality inequalities we prove the existence of optimal (deterministic) stationary policies by using the Dynkin formula. Moreover, we present a ``semimartingale characterization'' of an optimal stationary policy. Finally, we use a generalized Potlach process with control to illustrate the difference between our conditions and those in the previous literature, and then further apply our results to average optimal control problems of generalized birth--death systems, upwardly skip-free processes and two queueing systems. The approach developed in this paper is slightly different from the ``optimality inequality approach'' widely used in the previous literature.Comment: Published at http://dx.doi.org/10.1214/105051606000000105 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discrete-time controlled markov processes with average cost criterion: a survey

This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation

Reinforcement Learning: A Survey

This paper surveys the field of reinforcement learning from a computer-science perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem faced by an agent that learns behavior through trial-and-error interactions with a dynamic environment. The work described here has a resemblance to work in psychology, but differs considerably in the details and in the use of the word ``reinforcement.'' The paper discusses central issues of reinforcement learning, including trading off exploration and exploitation, establishing the foundations of the field via Markov decision theory, learning from delayed reinforcement, constructing empirical models to accelerate learning, making use of generalization and hierarchy, and coping with hidden state. It concludes with a survey of some implemented systems and an assessment of the practical utility of current methods for reinforcement learning.Comment: See http://www.jair.org/ for any accompanying file

Certified Reinforcement Learning with Logic Guidance

This paper proposes the first model-free Reinforcement Learning (RL) framework to synthesise policies for unknown, and continuous-state Markov Decision Processes (MDPs), such that a given linear temporal property is satisfied. We convert the given property into a Limit Deterministic Buchi Automaton (LDBA), namely a finite-state machine expressing the property. Exploiting the structure of the LDBA, we shape a synchronous reward function on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces that probabilistically satisfy the linear temporal property. This probability (certificate) is also calculated in parallel with policy learning when the state space of the MDP is finite: as such, the RL algorithm produces a policy that is certified with respect to the property. Under the assumption of finite state space, theoretical guarantees are provided on the convergence of the RL algorithm to an optimal policy, maximising the above probability. We also show that our method produces ''best available'' control policies when the logical property cannot be satisfied. In the general case of a continuous state space, we propose a neural network architecture for RL and we empirically show that the algorithm finds satisfying policies, if there exist such policies. The performance of the proposed framework is evaluated via a set of numerical examples and benchmarks, where we observe an improvement of one order of magnitude in the number of iterations required for the policy synthesis, compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782

Stochastic Tools for Network Security: Anonymity Protocol Analysis and Network Intrusion Detection

With the rapid development of Internet and the sharp increase of network crime, network security has become very important and received a lot of attention. In this dissertation, we model security issues as stochastic systems. This allows us to find weaknesses in existing security systems and propose new solutions. Exploring the vulnerabilities of existing security tools can prevent cyber-attacks from taking advantages of the system weaknesses. We consider The Onion Router (Tor), which is one of the most popular anonymity systems in use today, and show how to detect a protocol tunnelled through Tor. A hidden Markov model (HMM) is used to represent the protocol. Hidden Markov models are statistical models of sequential data like network traffic, and are an effective tool for pattern analysis. New, flexible and adaptive security schemes are needed to cope with emerging security threats. We propose a hybrid network security scheme including intrusion detection systems (IDSs) and honeypots scattered throughout the network. This combines the advantages of two security technologies. A honeypot is an activity-based network security system, which could be the logical supplement of the passive detection policies used by IDSs. This integration forces us to balance security performance versus cost by scheduling device activities for the proposed system. By formulating the scheduling problem as a decentralized partially observable Markov decision process (DEC-POMDP), decisions are made in a distributed manner at each device without requiring centralized control. When using a HMM, it is important to ensure that it accurately represents both the data used to train the model and the underlying process. Current methods assume that observations used to construct a HMM completely represent the underlying process. It is often the case that the training data size is not large enough to adequately capture all statistical dependencies in the system. It is therefore important to know the statistical significance level that the constructed model represents the underlying process, not only the training set. We present a method to determine if the observation data and constructed model fully express the underlying process with a given level of statistical significance. We apply this approach to detecting the existence of protocols tunnelled through Tor. While HMMs are a powerful tool for representing patterns allowing for uncertainties, they cannot be used for system control. The partially observable Markov decision process (POMDP) is a useful choice for controlling stochastic systems. As a combination of two Markov models, POMDPs combine the strength of HMM (capturing dynamics that depend on unobserved states) and that of Markov decision process (MDP) (taking the decision aspect into account). Decision making under uncertainty is used in many parts of business and science. We use here for security tools. We propose three approximation methods for discrete-time infinite-horizon POMDPs. One of the main contributions of our work is high-quality approximation solution for finite-space POMDPs with the average cost criterion, and their extension to DEC-POMDPs. The solution of the first algorithm is built out of the observable portion when the underlying MDP operates optimally. The other two methods presented here can be classified as the policy-based approximation schemes, in which we formulate the POMDP planning as a quadratically constrained linear program (QCLP), which defines an optimal controller of a desired size. This representation allows a wide range of powerful nonlinear programming (NLP) algorithms to be used to solve POMDPs. Simulation results for a set of benchmark problems illustrate the effectiveness of the proposed method. We show how this tool could be used to design a network security framework