The honeynet is a promising active cyber defense mechanism. It reveals the fundamental Indicators of Compromise (IoC) by luring attackers to conduct adversarial behaviors in a controlled and monitored environment. The active interaction at the honeynet brings a high reward but also introduces high implementation costs and risks of adversarial honeynet exploitation. In this work, we apply the infinite-horizon Semi-Markov Decision Process (SMDP) to characterize the stochastic transition and sojourn time of attackers in the honeynet and quantify the reward-risk trade-off. In particular, we produce adaptive long-term engagement policies shown to be risk-averse, cost-effective, and time-efficient. Numerical results have demonstrated that our adaptive interaction policies can quickly attract attackers to the target honeypot and engage them for a sufficiently long period to obtain worthy threat information. Meanwhile, the penetration probability is kept at a low level. The results show that the expected utility is robust against attackers of a large range of persistence and intelligence. Finally, we apply reinforcement learning to SMDP to solve the curse of modeling. Under a prudent choice of the learning rate and exploration policy, we achieve a quick and robust convergence of the optimal policy and value.
SMDP generalizes MDP by considering the random sojourn time at each state, and is widely applied to machine maintenance @cite_13 , resource allocation @cite_8 , and cybersecurity @cite_9 . However, as far as we know, it is the first time that the SMDP is applied to determine the optimal attacker engagement policy and to quantify the trade-off between the investigation reward and the risks.
@cite_9 @cite_13 @cite_8
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We consider a distributed server system with m servers operating under the processor sharing (PS) discipline. A stream of fixed size tasks arrives to a dispatcher, which assigns each task to one of the servers. We are interested in minimizing the mean sojourn time, i.e., the mean response time. To this end, we first analyze an M D l-PS queue in the MDP framework. In particular, we derive a closed form expression for the so-called size-aware relative value of state, which sums up the deviation from the average rate at which sojourn times are accumulated in the infinite time horizon. This result can be applied in numerous situations. Here we give an example in the context of dispatching problems by deriving efficient and robust state-dependent dispatching policies for homogeneous and heterogeneous server systems. The obtained policies are further demonstrated by numerical examples. Learning, planning, and representing knowledge at multiple levels of temporal ab- straction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforce- ment learning and Markov decision processes (MDPs). We extend the usual notion of action in this framework to include options—closed-loop policies for taking ac- tion over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as mus- cle twitches and joint torques. Overall, we show that options enable temporally abstract knowledge and action to be included in the reinforcement learning frame- work in a natural and general way. In particular, we show that options may be used interchangeably with primitive actions in planning methods such as dynamic pro- gramming and in learning methods such as Q-learning. Formally, a set of options defined over an MDP constitutes a semi-Markov decision process (SMDP), and the theory of SMDPs provides the foundation for the theory of options. However, the most interesting issues concern the interplay between the underlying MDP and the SMDP and are thus beyond SMDP theory. We present results for three such cases: 1) we show that the results of planning with options can be used during execution to interrupt options and thereby perform even better than planned, 2) we introduce new intra-option methods that are able to learn about an option from fragments of its execution, and 3) we propose a notion of subgoal that can be used to improve the options themselves. All of these results have precursors in the existing literature; the contribution of this paper is to establish them in a simpler and more general setting with fewer changes to the existing reinforcement learning framework. In particular, we show that these results can be obtained without committing to (or ruling out) any particular approach to state abstraction, hierarchy, function approximation, or the macro-utility problem. We consider the dispatching problem in a size- and state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By size- and state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on minimizing the mean sojourn time (i.e., response time) by an MDP approach. First we derive the so-called size-aware relative values of states with respect to the sojourn time in an M G 1 queue operating under FIFO, LIFO, SPT or SRPT disciplines. For FIFO and LIFO, the size-aware relative values turn out to be insensitive to the form of the job size distribution. The relative values are then exploited in developing efficient dispatching rules in the spirit of the first policy iteration. We consider a distributed server system in which heterogeneous servers operate under the processor sharing (PS) discipline. Exponentially distributed jobs arrive to a dispatcher, which assigns each task to one of the servers. In the so-called size-aware system, the dispatcher is assumed to know the remaining service requirements of some or all of the existing jobs in each server. The aim is to minimize the mean sojourn time, i.e., the mean response time. To this end, we first analyze an M M 1-PS queue in the framework of Markov decision processes, and derive the so-called size-aware relative value of state, which sums up the deviation from the average rate at which sojourn times are accumulated in the infinite time horizon. This task turns out to be non-trivial. The exact analysis yields an infinite system of first order differential equations, for which an explicit solution is derived. The relative values are then utilized to develop efficient dispatching policies by means of the first policy iteration (FPI). Numerically, we show that for the exponentially distributed job sizes the myopic approach, ignoring the future arrivals, yields an efficient and robust policy when compared to other heuristics. However, in the case of highly asymmetric service rates, an FPI based policy outperforms it. Additionally, the size-aware relative value of an M G 1-PS queue is shown to be sensitive with respect to the form of job size distribution, and indeed, the numerical experiments with constant job sizes confirm that the optimal decision depends on the job size distribution. A critical issue for the application of Markov decision processes (MDPs) to realistic problems is how the complexity of planning scales with the size of the MDP. In stochastic environments with very large or infinite state spaces, traditional planning and reinforcement learning algorithms may be inapplicable, since their running time typically grows linearly with the state space size in the worst case. In this paper we present a new algorithm that, given only a generative model (a natural and common type of simulator) for an arbitrary MDP, performs on-line, near-optimal planning with a per-state running time that has no dependence on the number of states. The running time is exponential in the horizon time (which depends only on the discount factor γ and the desired degree of approximation to the optimal policy). Our algorithm thus provides a different complexity trade-off than classical algorithms such as value iteration—rather than scaling linearly in both horizon time and state space size, our running time trades an exponential dependence on the former in exchange for no dependence on the latter. Our algorithm is based on the idea of sparse sampling. We prove that a randomly sampled look-ahead tree that covers only a vanishing fraction of the full look-ahead tree nevertheless suffices to compute near-optimal actions from any state of an MDP. Practical implementations of the algorithm are discussed, and we draw ties to our related recent results on finding a near-best strategy from a given class of strategies in very large partially observable MDPs (Kearns, Mansour, & Ng. Neural information processing systems 13, to appear). We consider the problem of power allocation over one or more time-varying channels with unknown distributions in energy harvesting communications. In the single-channel case, the transmitter chooses the transmit power based on the amount of stored energy in its battery with the goal of maximizing the average rate over time. We model this problem as a Markov decision process (MDP) with transmitter as the agent, battery status as the state, transmits power as the action and rate as the reward. The average reward maximization problem can be modeled by a linear program (LP) that uses the transition probabilities for the state-action pairs and their reward values to select a power allocation policy. This problem is challenging because the uncertainty in channels implies that the mean rewards associated with the state-action pairs are unknown. We therefore propose two online learning algorithms: linear program of sample means (LPSM) and Epoch-LPSM that learn these rewards and adapt their policies over time. For both algorithms, we prove that their regret is upper-bounded by a constant. To our knowledge this is the first result showing constant regret learning algorithms for MDPs with unknown mean rewards. We also prove an even stronger result about LPSM: that its policy matches the optimal policy exactly in finite expected time. Epoch-LPSM incurs a higher regret compared with the LPSM, while reducing the computational requirements substantially. We further consider a multi-channel scenario, where the agent also chooses a channel in each slot, and present our multi-channel LPSM (MC-LPSM) algorithm that explores different channels and uses that information to solve the LP during exploitation. MC-LPSM incurs a regret that scales logarithmically in time and linearly in the number of channels. Through a matching lower bound on the regret of any algorithm, we also prove the asymptotic order optimality of MC-LPSM. In the context of standard Markov decision processes (MDPs), the connection between Dynamic Program (DP) and Linear Program (LP) is well understood and is well established under sufficiently general conditions. LP based approach facilitates solving the constrained MDPs. Multiplicative or Risk sensitive MDPs, introduced to control the fluctuations variations around the expected value, are relatively less studied objects. DP equations are considerably well understood even in the context of Risk MDPs, however the LP connection is not known. We consider a finite horizon risk MDP problem and establish the connections between the DP and LP approaches. We augment the state space with a suitable component, to obtain the optimal policies for constrained risk MDPs. We apply this results to a server selection problem in Ber M K K queues, with a constraint on the utilization of the fast server. We discuss some interesting structural properties of the risk optimal policies. We study the problem of online learning in finite episodic Markov decision processes (MDPs) where the loss function is allowed to change between episodes. The natural performance measure in this learning problem is the regret defined as the difference between the total loss of the best stationary policy and the total loss suffered by the learner. We assume that the learner is given access to a finite action space A and the state space X has a layered structure with L layers, so that state transitions are only possible between consecutive layers. We describe a variant of the recently proposed Relative Entropy Policy Search algorithm and show that its regret after T episodes is 2√L|X||A|T log (|X||A| L) in the bandit setting and 2L √T log(|X||A| L) in the full information setting, given that the learner has perfect knowledge of the transition probabilities of the underlying MDP. These guarantees largely improve previously known results under much milder assumptions and cannot be significantly improved under general assumptions. In this paper, a low-complexity delay-aware cross-layer scheduling algorithm for two-hop relay communication systems is proposed. The complex interactions of the queues at the source node and the M relay nodes (RSs) are modeled as an infinite horizon average reward Markov decision process (MDP), whose state space involves the joint queue state information (QSI) of the queues at the source node and the M RSs as well as the joint channel state information (CSI) of all S-R and R-D links. To address the curse of dimensionality, an equivalent MDP formulation is first proposed, where the system state depends only on global QSI. Furthermore, using approximate MDP and stochastic learning, an auction-based distributed online learning algorithm is derived, where each node iteratively estimates a per-node value function based on real-time observations of the local CSI and local QSI as well as signaling between relays. The combined distributed learning converges almost surely to a global optimal solution for large arrivals. Finally, it is showed by simulations that the proposed scheme achieves significant gain compared with various baselines such as the conventional CSIT-only control and the throughput optimal control (in stability sense). This thesis addresses the question of planning under uncertainty within a time-dependent changing environment. Original motivation for this work came from the problem of building an autonomous agent able to coordinate with its uncertain environment; this environment being composed of other agents communicating their intentions or non-controllable processes for which some discrete-event model is available. We investigate several approaches for modeling continuous time-dependency in the framework of Markov Decision Processes (MDPs), leading us to a definition of Temporal Markov Decision Problems. Then our approach focuses on two separate paradigms. First, we investigate time-dependent problems as processes and describe them through the formalism of Time-dependent MDPs (TMDPs). We extend the existing results concerning optimality equations and present a new Value Iteration algorithm based on piecewise polynomial function representations in order to solve a more general class of TMDPs. This paves the way to a more general discussion on parametric actions in hybrid state and action spaces MDPs with continuous time. In a second time, we investigate the option of separately modeling the concurrent contributions of exogenous events. This approach of modeling leads to the use of Generalized Semi-Markov Decision Processes (GSMDP). We establish a link between the general framework of Discrete Events Systems Specification (DEVS) and the formalism of GSMDP, allowing us to build sound discrete-event compatible simulators. Then we introduce a simulation-based Policy Iteration approach for explicit-event Temporal Markov Decision Problems. This algorithmic contribution brings together results from simulation theory, forward search in MDPs, and statistical learning theory. The implicit-event approach was tested on a specific version of the Mars rover planning problem and on a drone patrol mission planning problem while the explicit-event approach was evaluated on a subway network control problem. In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state when the policy is pursued. We consider the problem of finding good policies whose risk is smaller than some user-specified threshold, and formalize it as a constrained MDP with two criteria. The first criterion corresponds to the value function originally given. We will show that the risk can be formulated as a second criterion function based on a cumulative return, whose definition is independent of the original value function. We present a model free, heuristic reinforcement learning algorithm that aims at finding good deterministic policies. It is based on weighting the original value function and the risk. The weight parameter is adapted in order to find a feasible solution for the constrained problem that has a good performance with respect to the value function. The algorithm was successfully applied to the control of a feed tank with stochastic inflows that lies upstream of a distillation column. This control task was originally formulated as an optimal control problem with chance constraints, and it was solved under certain assumptions on the model to obtain an optimal solution. The power of our learning algorithm is that it can be used even when some of these restrictive assumptions are relaxed. Markov Decision Processes (MDPs) provide an extensive theoretical background for problems of decision-making under uncertainty. In order to maintain computational tractability, however, real-world problems are typically discretized in states and actions as well as in time. Assuming synchronous state transitions and actions at fixed rates may result in models which are not strictly Markovian, or where agents are forced to idle between actions, losing their ability to react to sudden changes in the environment. In this work, we explore the application of Generalized Semi-Markov Decision Processes (GSMDPs) to a realistic multi-robot scenario. A case study will be presented in the domain of cooperative robotics, where real-time reactivity must be preserved, and synchronous discrete-time approaches are therefore sub-optimal. This case study is tested on a team of real robots, and also in realistic simulation. By allowing asynchronous events to be modeled over continuous time, the GSMDP approach is shown to provide greater solution quality than its discrete-time counterparts, while still being approximately solvable by existing methods. In this paper we consider the problem of computing an ϵ-optimal policy of a discounted Markov Decision Process (DMDP) provided we can only access its transition function through a generative sampling model that given any state-action pair samples from the transition function in O(1) time. Given such a DMDP with states , actions , discount factor γ∈(0,1), and rewards in range [0,1] we provide an algorithm which computes an ϵ-optimal policy with probability 1−δ where both the run time spent and number of sample taken is upper bounded by O[ | || | (1−γ)3ϵ2 log( | || | (1−γ)δϵ )log( 1 (1−γ)ϵ )] . For fixed values of ϵ, this improves upon the previous best known bounds by a factor of (1−γ)−1 and matches the sample complexity lower bounds proved in azar2013minimax up to logarithmic factors. We also extend our method to computing ϵ-optimal policies for finite-horizon MDP with a generative model and provide a nearly matching sample complexity lower bound. We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. Tasks that require many sequential decisions or complex solutions are hard to solve using conventional reinforcement learning algorithms. Based on the semi Markov decision process setting (SMDP) and the option framework, we propose a model which aims to alleviate these concerns. Instead of learning a single monolithic policy, the agent learns a set of simpler sub-policies as well as the initiation and termination probabilities for each of those sub-policies. While existing option learning algorithms frequently require manual specification of components such as the sub-policies, we present an algorithm which infers all relevant components of the option framework from data. Furthermore, the proposed approach is based on parametric option representations and works well in combination with current policy search methods, which are particularly well suited for continuous real-world tasks. We present results on SMDPs with discrete as well as continuous state-action spaces. The results show that the presented algorithm can combine simple sub-policies to solve complex tasks and can improve learning performance on simpler tasks. In this semi-tutorial paper, we first review the information-theoretic approach to account for the computational costs incurred during the search for optimal actions in a sequential decision-making problem. The traditional (MDP) framework ignores computational limitations while searching for optimal policies, essentially assuming that the acting agent is perfectly rational and aims for exact optimality. Using the free-energy, a variational principle is introduced that accounts not only for the value of a policy alone, but also considers the cost of finding this optimal policy. The solution of the variational equations arising from this formulation can be obtained using familiar Bellman-like value iterations from dynamic programming (DP) and the Blahut-Arimoto (BA) algorithm from rate distortion theory. Finally, we demonstrate the utility of the approach for generating hierarchies of state abstractions that can be used to best exploit the available computational resources. A numerical example showcases these concepts for a path-planning problem in a grid world environment. The multi-armed bandit (MAB) problem features the classical tradeoff between exploration and exploitation. The input specifies several stochastic arms which evolve with each pull, and the goal is to maximize the expected reward after a fixed budget of pulls. The celebrated work of , surveyed in [8], presumes a condition on the arms called the martingale assumption. In [9], A. obtained an LP-based 1 48-approximation for the problem with the martingale assumption removed. We improve the algorithm to a 4 27-approximation, with simpler analysis. Our algorithm also generalizes to the case of MAB superprocesses with (stochastic) multi-period actions. This generalization captures the framework introduced by Guha and Munagala in [11], and yields new results for their budgeted learning problems. Also, we obtain a (1 2 -- e)-approximation for the variant of MAB where preemption (playing an arm, switching to another arm, then coming back to the first arm) is not allowed. This contains the stochastic knapsack problem of Dean, Goemans, and Vondrak in [6] with correlated rewards, where we are given a knapsack of fixed size, and a set of jobs each with a joint distribution for its size and reward. The actual size and reward of a job can only be discovered in real-time as it is being scheduled, and the objective is to maximize expected reward before the knapsack size is exhausted. Our (1 2 -- e)-approximation improves the 1 16 and 1 8 approximations in [9] for correlated stochastic knapsack with cancellation and no cancellation, respectively, providing to our knowledge the first tight algorithm for these problems that matches the integrality gap of 2. We sample probabilities from an exponential-sized dynamic programming solution, whose existence is guaranteed by an LP projection argument. We hope this technique can also be applied to other dynamic programming problems which can be projected down onto a small LP. The complex interconnections between various critical infrastructure sectors make the system of systems (SoS) vulnerable to failures and highlight the importance of robustness and resilience. To this end, we first establish holistic probabilistic networks to model the interdependencies between infrastructure components. To capture the underlying failure and recovery dynamics, we further propose a Markov decision processes (MDP) model in which the response policy determines a long-term performance. To address the challenge of a large dimensionality, we exploit the sparsity of the network interconnections and solve an approximate linear program by the variable elimination, which leads to a distributed control policy under mild assumptions. Finally, we use a case study of the interdependent power and subway systems to corroborate the results and show that the optimal resilience resource planning and allocation can reduce the failure probability and mitigate the impact of failures caused by natural or artificial disasters. In this paper, we propose an optimization framework of offloading from a single mobile device (MD) to multiple edge devices. We aim to minimize both total tasks’ execution latency and the MD’s energy consumption by jointly optimizing the task allocation decision and the MD’s central process unit (CPU) frequency. This paper considers two cases for the MD, i.e., fixed CPU frequency and elastic CPU frequency. Since these problems are NP-hard, we propose a linear relaxation-based approach and a semidefinite relaxation (SDR)-based approach for the fixed CPU frequency case, and an exhaustive search-based approach and an SDR-based approach for the elastic CPU frequency case. Our simulation results show that the SDR-based algorithms achieve near optimal performance. Performance improvement can be obtained with the proposed scheme in terms of energy consumption and tasks’ execution latency when multiple edge devices and elastic CPU frequency are considered. Finally, we show that the MD’s flexible CPU range can have an impact on the task allocation. We formulate the problem of network-coding (NC)-based scheduling for media transmission to multiple users over a wireless-local-area-network-like or WiMAX-like network as a Markov decision process (MDP). NC is used to minimize the packet losses that resulted from unreliable wireless channel conditions, whereas the MDP is employed to find the optimal policy for transmissions of unequally important media packets. Based on this, a dynamic programming technique is used to give an optimal transmission policy. However, this dynamic programming technique quickly leads to computational intractability, even for scenarios with a moderate number of receivers. To address this problem, we further propose a simulation-based dynamic programming algorithm that has a much lower run time yet empirically converges quickly to the optimal solution.