Policies For Markov Decision Processes Research Articles

Learning to construct a solution for UAV path planning problem with positioning error correction

Unmanned aerial vehicles (UAVs) are advanced flight systems. However, their positioning systems cause distance-dependent errors during flight. This study seeks to solve the UAV path planning problem with positioning error correction (UPEC) with an end-to-end method. Traditional methods struggle to balance solution quality and computational overload, and often have limited utilisation of scenario information. To overcome these issues, we propose a path planning model (PPM) based on deep reinforcement learning to solve the UPEC. The model has a complete structure that includes a mathematical model, feature engineering, solution process, neural policy network, scenario generation, training process, and test solution mechanism. Specifically, we first establish a Markov decision process (MDP) for UPEC and apply feature engineering with effective features to support decision-making. We then introduce a path planning neural network (PPNN) to represent the MDP policy. Based on the dataset generated from the multi-rule combination validation, we train the PPNN using the proposed RL algorithm with storage pool. Furthermore, we propose a backtracking mechanism to guarantee solution feasibility during the construction process. Extensive experiments demonstrate that the proposed PPM outperforms existing state-of-the-art algorithms in terms of solution quality and timeliness, and the backtracking mechanism effectively improves the scenario completion rate. The model study indicates the efficacy of our training algorithm and the generalisation of the PPNN. Additionally, our construction process is problem-tailored and more suitable for addressing UPEC than iterative search algorithms, because it effectively mitigates the impact of invalid nodes.

Modified monotone policy iteration for interpretable policies in Markov decision processes and the impact of state ordering rules

Modified monotone policy iteration for interpretable policies in Markov decision processes and the impact of state ordering rules

Sparse randomized policies for Markov decision processes based on Tsallis divergence regularization

This work investigates a somewhat different point of view on Markov decision processes by reinterpreting them as a randomized shortest paths problem on a bipartite graph, therefore establishing bridges with entropy-regularized reinforcement learning. The graph structure contains the set of states as “left” nodes and the set of actions as “right” nodes. In that context, the action-to-state transition probabilities are provided by the environment whereas the state-to-action probabilities correspond to the (stochastic) policy to be found. The randomized shortest paths formalism (minimizing expected cost to the goal state subject to (Shannon or Tsallis) relative entropy regularization) is then readily applied to this bipartite structure, providing a possibly sparse stochastic policy interpolating between a least-cost and a purely random policy. The algorithm computing the policy is closely related to the dual linear programming formulation of the Markov decision processes to which the relative entropy regularization term, multiplied by a scaling factor balancing exploitation and exploration (the temperature), is added. It is derived from well-known techniques of discrete optimal control, relying on costates (Lagrange parameters) backward computation. In summary, the proposed algorithm allows the design of optimal stochastic – but still sparse – policies, ranging from a purely rational to a random behavior, depending on the temperature parameter.

Risk-Aware Markov Decision Process Contingency Management Autonomy for Uncrewed Aircraft Systems

Uncrewed aircraft systems (UASs) are being increasingly adopted for a variety of applications. The risk UAS poses to people and property must be kept to acceptable levels. This paper proposes risk-aware contingency management autonomy to prevent an accident in the event of component malfunction, specifically propulsion unit failure and/or battery degradation. The proposed autonomy is modeled as a Markov decision process (MDP), whose solution is a contingency management policy that appropriately executes emergency landing, flight termination, or continuation of planned flight actions. Motivated by the potential for errors in fault/failure indicators, the partial observability of the MDP state space is investigated. The performance of optimal policies is analyzed over varying observability conditions in a high-fidelity simulator. Results indicate that both partially observable MDP and maximum a posteriori MDP policies had similar performance over different state observability criteria, given the nearly deterministic state transition model.

Risk-Averse Decision Making Under Uncertainty

A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others. In this paper, we consider the problem of designing policies for MDPs and POMDPs with objectives and constraints in terms of dynamic coherent risk measures rather than the traditional total expectation, which we refer to as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constrained risk-averse problem</i> . Our contributions can be described as follows: For MDPs, under some mild assumptions, we propose an optimization-based method to synthesize Markovian policies. We then demonstrate that such policies can be found by solving difference convex programs (DCPs). We show that our formulation generalize linear programs for constrained MDPs with total discounted expected costs and constraints; For POMDPs, we show that, if the coherent risk measures can be defined as a Markov risk transition mapping, an infinite-dimensional optimization can be used to design Markovian belief-based policies. For POMDPs with stochastic finite-state controllers (FSCs), we show that the latter optimization simplifies to a (finite-dimensional) DCP. We incorporate these DCPs in a policy iteration algorithm to design risk-averse FSCs for POMDPs. We demonstrate the efficacy of the proposed method with numerical experiments involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) risk measures.

DSMC Evaluation Stages: Fostering Robust and Safe Behavior in Deep Reinforcement Learning – Extended Version

Neural networks (NN) are gaining importance in sequential decision-making. Deep reinforcement learning (DRL), in particular, is extremely successful in learning action policies in complex and dynamic environments. Despite this success, however, DRL technology is not without its failures, especially in safety-critical applications: (i) the training objective maximizes average rewards, which may disregard rare but critical situations and hence lack local robustness; (ii) optimization objectives targeting safety typically yield degenerated reward structures, which, for DRL to work, must be replaced with proxy objectives. Here, we introduce a methodology that can help to address both deficiencies. We incorporate evaluation stages (ES) into DRL, leveraging recent work on deep statistical model checking (DSMC), which verifies NN policies in Markov decision processes. Our ES apply DSMC at regular intervals to determine state space regions with weak performance. We adapt the subsequent DRL training priorities based on the outcome, (i) focusing DRL on critical situations and (ii) allowing to foster arbitrary objectives. We run case studies on two benchmarks. One of them is the Racetrack, an abstraction of autonomous driving that requires navigating a map without crashing into a wall. The other is MiniGrid, a widely used benchmark in the AI community. Our results show that DSMC-based ES can significantly improve both (i) and (ii).

Asymptotic Optimality of Semi-Open-Loop Policies in Markov Decision Processes with Large Lead Times

A generic way to verify asymptotic optimality of semi-open-loop policies for a wide class of MDPs with large lead times. In many real-life inventory models, order lead times can result in uncertain effects of inventory decisions. However, as the lead time grows large, one would naturally postulate that the effect of the delayed order depends weakly on the current inventory level and, thus, intuit that decoupling the delayed order with the current inventory level may provide good heuristics. Motivated by these examples, in “Asymptotic Optimality of Semi-open-Loop Policies in Markov Decision Processes with Large Lead Times,” Bai et al. consider a generic Markov decision process (MDP) with one delayed control and one immediate control. For MDPs defined on general spaces with uniformly bounded cost functions and a fast mixing property, they construct a periodic semi-open-loop policy for each lead time value and show that these policies are asymptotically optimal as the lead time goes to infinity. For MDPs defined on Euclidean spaces with linear dynamics and convex structures, they impose another set of conditions under which constant delayed-control policies are asymptotically optimal.

Asymptotic Optimality of Semi-Open-Loop Policies in Markov Decision Processes with Large Lead Times

A generic way to verify asymptotic optimality of semi-open-loop policies for a wide class of MDPs with large lead times. In many real-life inventory models, order lead times can result in uncertain effects of inventory decisions. However, as the lead time grows large, one would naturally postulate that the effect of the delayed order depends weakly on the current inventory level and, thus, intuit that decoupling the delayed order with the current inventory level may provide good heuristics. Motivated by these examples, in “Asymptotic Optimality of Semi-open-Loop Policies in Markov Decision Processes with Large Lead Times,” Bai et al. consider a generic Markov decision process (MDP) with one delayed control and one immediate control. For MDPs defined on general spaces with uniformly bounded cost functions and a fast mixing property, they construct a periodic semi-open-loop policy for each lead time value and show that these policies are asymptotically optimal as the lead time goes to infinity. For MDPs defined on Euclidean spaces with linear dynamics and convex structures, they impose another set of conditions under which constant delayed-control policies are asymptotically optimal.

Entropy Rate Maximization of Markov Decision Processes for Surveillance Tasks⋆

We consider the problem of synthesizing optimal policies for Markov decision processes (MDP) for both utility objective and security constraint. Specifically, our goal is to maximize the entropy rate of the MDP while achieving a surveillance task in the sense that a given region of interest is visited infinitely often with probability one (w.p.1). Such a policy is of our interest since it guarantees both the completion of tasks and maximizes the unpredictability of limit behavior of the system. Existing works either focus on the total entropy or do not consider the surveillance tasks which are not suitable for surveillance tasks with infinite horizon. We provide a complete solution to this problem. Specifically, we present an algorithm for synthesizing entropy rate maximizing policies for communicating MDPs. Then based on a new state classification method, we show the entropy rate maximization problem under surveillance task can be effectively solved in polynomial-time. We illustrate the proposed algorithm based on a case study of robot planning scenario.

Economic MPC of Markov Decision Processes: Dissipativity in undiscounted infinite-horizon optimal control

Economic Model Predictive Control (MPC) dissipativity theory is central to discussing the stability of policies resulting from minimizing economic stage costs. In its current form, the dissipativity theory for economic MPC applies to problems based on deterministic dynamics or to very specific classes of stochastic problems, and does not readily extend to generic Markov decision processes. In this paper, we clarify the core reason for this difficulty, and propose a generalization of the economic MPC dissipativity theory that circumvents it. This generalization focuses on undiscounted infinite-horizon problems and is based on nonlinear stage cost functionals, allowing one to discuss the Lyapunov asymptotic stability of policies for Markov decision processes in terms of the probability measures underlying their stochastic dynamics. This theory is illustrated for the stochastic linear quadratic regulator with Gaussian process noise, for which a storage functional can be provided explicitly. For the sake of brevity, we limit our discussion to undiscounted Markov decision processes.

Online shielding for reinforcement learning

Besides the recent impressive results on reinforcement learning (RL), safety is still one of the major research challenges in RL. RL is a machine-learning approach to determine near-optimal policies in Markov decision processes (MDPs). In this paper, we consider the setting where the safety-relevant fragment of the MDP together with a temporal logic safety specification is given, and many safety violations can be avoided by planning ahead a short time into the future. We propose an approach for online safety shielding of RL agents. During runtime, the shield analyses the safety of each available action. For any action, the shield computes the maximal probability to not violate the safety specification within the next k steps when executing this action. Based on this probability and a given threshold, the shield decides whether to block an action from the agent. Existing offline shielding approaches compute exhaustively the safety of all state-action combinations ahead of time, resulting in huge computation times and large memory consumption. The intuition behind online shielding is to compute at runtime the set of all states that could be reached in the near future. For each of these states, the safety of all available actions is analysed and used for shielding as soon as one of the considered states is reached. Our approach is well-suited for high-level planning problems where the time between decisions can be used for safety computations and it is sustainable for the agent to wait until these computations are finished. For our evaluation, we selected a 2-player version of the classical computer game Snake. The game represents a high-level planning problem that requires fast decisions and the multiplayer setting induces a large state space, which is computationally expensive to analyse exhaustively.

AdaPool: A Diurnal-Adaptive Fleet Management Framework Using Model-Free Deep Reinforcement Learning and Change Point Detection

This paper introduces an adaptive model-free deep reinforcement approach that can recognize and adapt to the diurnal patterns in the ride-sharing environment with car-pooling. Deep Reinforcement Learning (RL) suffers from catastrophic forgetting due to being agnostic to the timescale of changes in the distribution of experiences. Although RL algorithms are guaranteed to converge to optimal policies in Markov decision processes (MDPs), this only holds in the presence of static environments. However, this assumption is very restrictive. In many real-world problems like ride-sharing, traffic control, etc., we are dealing with highly dynamic environments, where RL methods yield only sub-optimal decisions. To mitigate this problem in highly dynamic environments, we (1) adopt an online Dirichlet change point detection (ODCP) algorithm to detect the changes in the distribution of experiences, (2) develop a Deep Q Network (DQN) agent that is capable of recognizing diurnal patterns and making informed dispatching decisions according to the changes in the underlying environment. Rather than fixing patterns by time of week, the proposed approach automatically detects that the MDP has changed, and uses the results of the new model. In addition to the adaptation logic in dispatching, this paper also proposes a dynamic, demand aware vehicle-passenger matching and route planning framework that dynamically generates optimal routes for each vehicle based on online demand, vehicle capacities, and locations. Evaluation on New York City Taxi public dataset shows the effectiveness of our approach in improving the fleet utilization, where less than 50&#x0025; of the fleet are utilized to serve the demand of up to 90&#x0025; of the requests, while maximizing profits and minimizing idle times.

A Reinforcement Learning Approach for Optimizing the Age-of-Computing-Enabled IoT

Age of Information (AoI) is a newly rising metric for measuring the freshness of information. In this article, we consider a multidevice computing-enabled Internet of Things (IoT) system with a common destination, in which the status update sampled by the device can be offloaded directly to the destination for computing or computed by the device and then delivered to the destination, and jointly design offloading and scheduling policies to minimize the average weighted sum of AoI and energy consumption. The challenge lies in computing mode selection and its strong coupling with scheduling decisions. To address this issue, we formulate the optimization problem as a bilevel discrete-time Markov decision process (MDP) and approximate the optimal solution by relative value iteration. Furthermore, the threshold structure of the MDP policy is shown. However, with the expansion of the system scale, the MDP policy will suffer from the curse of dimensionality. In light of this, we develop a learning-based algorithm based on emerging deep reinforcement learning (DRL) to reduce the dimensionality of state space and utilize a late experience storage method to train two heterogeneous artificial neural networks (ANNs) synchronously during the training process. Simulation results show the structure of the MDP policy and verify the performance of the DRL policy is near-optimal.

Efficient algorithms for Risk-Sensitive Markov Decision Processes with limited budget

We tackle the problem of finding optimal policies for Markov Decision Processes, that minimize the probability of the cumulative cost exceeding a given budget. Such task falls under the umbrella of Risk-Sensitive Markov Decision Processes, which optimize a non-additive, non-linear function of cumulative cost that incorporates the user's attitude towards risk. Current algorithms for solving that task, for any budget equal or smaller than an user-defined budget, scale poorly when the support of the cost function is large, since they operate in an augmented state space which enumerates all possible remaining budgets. To circumvent this issue, we develop (i) an improved version of the Topological Value Iteration with Dynamic Programming algorithm (tvi-dp), and (ii) the first symbolic dynamic programming algorithm for this class of problems, called rs-spudd, that exploits conditional independence in the transition function in the augmented state space. The proposed algorithms improve efficiency by pruning irrelevant states and terminating early, without sacrificing optimality. Empirical results show that rs-spudd is able to solve problems up to 103 times larger than tvi-dp.

Reducible Markov Decision Processes and Stochastic Games

Markov decision processes (MDPs) provide a powerful framework for analyzing dynamic decision making. However, their applications are significantly hindered by the difficulty of obtaining solutions. In this study, we introduce reducible MDPs whose exact solutions can be obtained by solving simpler MDPs, termed the coordinate MDPs. The value function and an optimal policy of a reducible MDP are linear functions of those of the associated coordinate MDP. Because the coordinate MDP does not involve the multi‐dimensional endogenous state, we achieve dimension reduction on a reducible MDP. Extending the MDP framework to multiple players, we introduce reducible stochastic games. We show that these games reduce to simpler coordinate games that do not involve the multi‐dimensional endogenous state. We specify sufficient conditions for the existence of a pure‐strategy Markov perfect equilibrium in reducible stochastic games and derive closed‐form expressions for the players’ equilibrium values. The reducible framework encompasses a variety of linear and nonlinear models and offers substantial simplification in analysis and computation. We provide guidelines and illustrative examples on formulating problems as reducible models. We demonstrate the applicability and modeling flexibility of reducible models in a wide range of contexts including capacity and inventory management and duopoly competition.

Reinforcement Learning Based Hierarchical Multi-Agent Robotic Search Team in Uncertain Environment

Field of robotics has been under the limelight because of recent advances in Artificial Intelligence (AI). Due to increased diversity in multi-agent systems, new models are being developed to handle complexity of such systems. However, most of these models do not address problems such as; uncertainty handling, efficient learning, agent coordination and fault detection. This paper presents a novel approach of implementing Reinforcement Learning (RL) on hierarchical robotic search teams. The proposed algorithm handles uncertainties in the system by implementing Q-learning and depicts enhanced efficiency as well as better time consumption compared to prior models. The reason for that is each agent can take action on its own thus there is less dependency on leader agent for RL policy. The performance of this algorithm is measured by introducing agents in an unknown environment with both Markov Decision Process (MDP) and RL policies at their disposal. Simulation-based comparison of the agent motion is presented using the results from of MDP and RL policies. Furthermore, qualitative comparison of the proposed model with prior models is also presented.

Constrained Risk-Averse Markov Decision Processes

We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.

Iterative Bounding MDPs: Learning Interpretable Policies via Non-Interpretable Methods

Current work in explainable reinforcement learning generally produces policies in the form of a decision tree over the state space. Such policies can be used for formal safety verification, agent behavior prediction, and manual inspection of important features. However, existing approaches fit a decision tree after training or use a custom learning procedure which is not compatible with new learning techniques, such as those which use neural networks. To address this limitation, we propose a novel Markov Decision Process (MDP) type for learning decision tree policies: Iterative Bounding MDPs (IBMDPs). An IBMDP is constructed around a base MDP so each IBMDP policy is guaranteed to correspond to a decision tree policy for the base MDP when using a method-agnostic masking procedure. Because of this decision tree equivalence, any function approximator can be used during training, including a neural network, while yielding a decision tree policy for the base MDP. We present the required masking procedure as well as a modified value update step which allows IBMDPs to be solved using existing algorithms. We apply this procedure to produce IBMDP variants of recent reinforcement learning methods. We empirically show the benefits of our approach by solving IBMDPs to produce decision tree policies for the base MDPs.

Context-Aware Adaptive Route Mutation Scheme: A Reinforcement Learning Approach

Moving target defense (MTD) is an emerging proactive defense technology, which can reduce the risk of vulnerabilities exploited by attacker. As a crucial component of MTD, route mutation (RM) faces a few fundamental problems defending against sophisticated Distributed-Denial of Service (DDoS) attacks: 1) it is unable to make optimal mutation selection due to insufficient learning in attack behaviors and 2) because network situation is time varying, RM also lacks self-adaptation in mutation parameters. In this article, we propose a context-aware Q-learning algorithm for RM (CQ-RM) that can learn attack strategies to optimize the selection of mutated routes. We first integrate four representative attack strategies into a unified mathematical model and formalize multiple network constraints. Then, taking above network constraints into considerations, we model RM process as a Markov decision process (MDP). To look for the optimal policy of MDP, we develop a context estimation mechanism and further propose the CQ-RM scheme, which can adjust learning rate and mutation period adaptively. Correspondingly, the optimal convergence of CQ-RM is proved theoretically. Finally, extensive experimental results highlight the effectiveness of our method compared to representative solutions.

Optimal Data Transfer of SEH-WSN Node via MDP Based on Duty Cycle and Battery Energy

Applications in wireless sensor networks (WSNs) are rapidly spreading out over the world. The one critical point of WSNs is energy consumption, where the transmitted data is limited by battery energy. Solar energy is used to handle the depletion of the battery energy via photo voltaic (PV) panels. A solar energy harvesting WSN (SEH-WSN) node utilizes exponential decision-dynamic duty cycle scheduling based on prospective increase in energy (ED-DSP) to save battery energy by adjusting the duty cycle from an exponential curve and future solar energy. To estimate the prospective solar energy, a prediction technique is applied, but does not guarantee 100% accuracy. Hence, this paper proposes a Markov Decision Process (MDP) to schedule a duty cycle of an SEH-WSN node instead of the ED-DSP depending on the predicted energy. We evaluate its performance via MATLAB simulations with simple irradiance models and real annual irradiance data. The results show that the MDP policy outperforms the ED-DSP.