Approximate Dynamic Programming

Introduction Reinforcement learning formalizes the concept of learning from interactions.1 Broadly, reinforcement learning focuses on a setting in which an agent (decision maker) sequentially interacts with an environment that is partially unknown to them. At each stage, the agent takes an action and receives a reward. The objective of the agent is to maximize rewards accumulated in the long run. There are many situations in health care where decisions are made sequentially for which reinforcement learning approaches could prove useful for decision making. Throughout this article, we consider treatment prescription as an archetypical example to connect reinforcement learning concepts to a health care setting. In this setting, the care provider, the prescribed treatment, and the patients can be viewed as the agent, the action, and the environment, respectively, as depicted in Figure 1.Figure 1: Sequential treatment of AKI or CKD complications modeled as a reinforcement learning problem.Background In this section, with the objective of making reinforcement learning literature more accessible to a clinical audience, we briefly introduce related fundamental concepts and approaches. We refer the interested reader to Sutton and Barto1 for a comprehensive introduction to reinforcement learning. Markov Decision Processes Markov decision processes (MDPs) are a formalism of the sequential decision-making problem that has been central to the theoretical and practical advancements of reinforcement learning. In each stage of an MDP, the agent observes the state of the environment and takes an action, which, in turn, results in a change of the state. This change of state is assumed to be probabilistic with the next state being determined only by the preceding state, the chosen action, and the transition probability. The agent also receives a reward that is a function of the taken action, the preceding state, and the subsequent state. In an MDP, the objective of the agent is to maximize the return defined as the reward accumulated over a time horizon. In some applications, it is common to consider the horizon to be infinite, in which case the future rewards are discounted by a factor smaller than one. The selection of action by the agent on the basis of the observed state is known as the policy. More formally, a policy is a probabilistic mapping from states to each possible action. Because the policy and the reward are a function of the state, it is critical to estimate the utility of being in a certain state. More specifically, the value function is defined as the expected return starting from a given state under the chosen policy. Under this formalism, the objective of the agent is to find the optimal policy that maximizes the value function for all states. Reinforcement Learning Methods Action-value methods are a class of reinforcement learning methods in which the actions are chosen on the basis of the estimation of their long-term value. A prominent example of an action-value method is Q-learning in which the agent iteratively takes actions with the highest estimated values and updates the action-state value function on the basis of new observations. Policy gradient methods are another class of reinforcement learning methods that seek to optimize the policy directly instead of choosing actions on the basis of their respective estimated value. Such methods could be advantageous in health care applications that entail a large number of possible actions, e.g., when recommending a wide range of drug dosages or treatment options. Clinical Applications Reinforcement learning frameworks and methods are broadly applicable to clinical settings in which decisions are made sequentially. A prominent clinical application of reinforcement learning is for treatment recommendation, which has been studied across a variety of diseases and treatments including radiation and chemotherapy for cancer, brain stimulation for epilepsy, and treatment strategies for sepsis.2–5 In such treatment recommendation settings, a policy is commonly known as a dynamic treatment regime. There are various other clinical applications of reinforcement learning including diagnosis, medical imaging, and decision support tools (see refs. 2–5 and the references therein). Reinforcement Learning in Nephrology Although there have been recent applications of machine learning in nephrology,6,7 to the best of the authors' knowledge, the application of reinforcement learning to nephrology has been primarily limited to optimizing the erythropoietin dosage in hemodialysis patients.8,9 However, there are other settings where reinforcement learning has the potential to improve patient care in nephrology. For example, reinforcement learning methods can be adopted in the treatment of the complications of AKI or CKD (Figure 1). In this problem, the state models the conditions of the patient (e.g., vital signs, laboratory test results including urine and blood tests, and urine output measurements). The action refers to the treatment options (e.g., the dosage of medications such as sodium polystyrene sulfonate, and hemodialysis). The reward models the improvement in patient conditions. Similarly, reinforcement learning can help automate and optimize the dosage of immunosuppressive drugs in kidney transplants. Challenges and Opportunities Despite the success of reinforcement learning in several simplified clinical settings, their large-scale application to patient care faces several open challenges. The complexity of human biology complicates modeling clinical decision making as a reinforcement learning problem. The state space in such settings is often enormous, which could make a purely computational approach infeasible. Moreover, modeling all potential objectives a priori as a reward function may not be feasible. To overcome these challenges and realize the potential of reinforcement learning, clinical insight can play a pivotal role. More specifically, restricting the state space to only include highly relevant clinical variables could greatly reduce the computational complexity. Furthermore, using inverse reinforcement learning,2 relevant reward functions can be learned from retrospective studies assuming the optimality of clinical decisions. Another critical challenge is addressing moral and ethical concerns. It is imperative to ensure that reinforcement learning methods do not cause harm to the patient. To this end, there exists a need for a thorough validation of such methods before their use in patient care. Hence, there is a need to go beyond retrospective studies that have been used for the proof of concept of most existing reinforcement learning methods in health care applications.2,3 The lessons learned from the success of reinforcement learning in other application areas (e.g., self-driving cars) can help navigate the path to realizing its potential in health care. Accessible open-source simulation environments that enable researchers to compare various approaches are essential to the field of reinforcement learning. OpenAI Gym is currently the leading toolkit containing a wide range of simulated environments, e.g., surgical robotics.10 The development of high-quality and reliable simulation environments for nephrology and other health care applications can facilitate the development and validation of reinforcement learning methods beyond limited retrospective studies. The adoption of methods validated in such simulation environments in actual clinical settings will require clinicians' oversight. Similar to how self-driving cars require a human driver to ensure collision avoidance, clinicians' oversight is critical to ensure the safety of the patients, especially in the early stages of the adoption of reinforcement learning methods. The data from clinicians' decisions (e.g., overruling the automated treatment recommendation) can be used to improve the reliability of autonomous systems over time and reduce the burden of clinicians' oversight.

The widespread deployment of smart meters and communication technologies brings opportunities to improve the adaptability and flexibility of future manufacturing systems under growing complexity and uncertainty. As a result, data-driven approaches, especially Reinforcement Learning (RL) methods, are gaining wide attention in recent years. Although in the current literature, RL approaches show superiority over traditional methods in many applications, a comprehensive review and comparison of different RL methods and their use in discrete manufacturing system control under changing environments have not yet been established. This paper first provides a literature review of RL algorithms for decision-making in discrete manufacturing systems, and then systematically discusses the underlying mechanisms of four most commonly used RL algorithms. In addition, the performance of these RL algorithms is compared by solving a production control problem, which aims to maximize the profit under time-varying production costs. The comparison results show that the single-agent RL methods with discrete action space can provide satisfactory results in small-scale systems, while multi-agent RL algorithms are more suitable to solve problems in complex, large-scale systems to remit the curse of dimensionality. This research sheds light on the impacts of RL method selection on the search for high-quality solutions in manufacturing systems, which is envisioned to drive future research on RL-supported manufacturing systems.

Reinforcement learning (RL) has shown promising performance in autonomous driving applications in recent years. The early end-to-end RL method is usually unexplainable and fails to generate stable actions, while the hierarchical RL (HRL) method can tackle the above issues by dividing complex problems into multiple sub-tasks. Prior HRL works either select discrete driving behaviors with continuous control commands, or generate expected goals for the low-level controller. However, they typically have strong scenario dependence or fail to generate goals with good quality. To address the above challenges, we propose a Continuous-Lattice Hierarchical RL (Cola-HRL) method for autonomous driving tasks to make high-quality decisions in various scenarios. We utilize the continuous-lattice module to generate reasonable goals, ensuring temporal and spatial reachability. Then, we train and evaluate our method under different traffic scenarios based on real-world High Definition maps. Experimental results show our method can handle multiple scenarios. In addition, our method also demonstrates better performance and driving behaviors compared to existing RL methods.

Adaptive bitrate (ABR) streaming algorithms play an important role in ensuring a high Quality of Experience (QoE) for the consumer. However, a lot of ABR algorithms tend to be too ad hoc. In response, methods based on a Markov Decision Process (MDP) offer more intelligent models. In particular, Reinforcement Learning (RL) methods typically do so via QoE metrics. However, RL methods are plagued by high complexity and long convergence times due to their model-free nature. This paper proposes qMDP, which is an RL method with an MDP partially modeled by an M/D/1/K queue. Our study shows that qMDP results in higher QoE and faster convergence compared to a QoE-only model-free version.

With the advent of the 5G era, due to the limited network resources and methods before, it cannot be guaranteed that all services can be carried out. In the 5G era, network services are not limited to mobile phones and computers but support the normal operation of equipment in all walks of life. There are more and more scenarios and more and more complex scenarios, and more convenient and fast methods are needed to assist network services. In order to better perform network offloading of the business, make the business more refined, and assist the better development of 5G network technology, this article proposes 5G network slicing: methods to support blockchain and reinforcement learning, aiming to improve the efficiency of network services. The research results of the article show the following: (1) In the model testing stage, the research results on the variation of the delay with the number of slices show that the delay increases with the increase of the number of slices, but the blockchain + reinforcement learning method has the lowest delay. The minimum delay can be maintained. When the number of slices is 3, the delay is 155 ms. (2) The comparison of the latency of different types of slices shows that the latency of 5G network slicing is lower than that of 4G, 3G, and 2G network slicing, and the minimum latency of 5G network slicing using blockchain and reinforcement learning is only 15 ms. (3) In the detection of system reliability, reliability decreases as the number of users increases because reliability is related to time delay. The greater the transmission delay, the lower the reliability. The reliability of supporting blockchain + reinforcement learning method is the highest, with a reliability of 0.95. (4) Through the resource utilization experiment of different slices, it can be known that the method of blockchain + reinforcement learning has the highest resource utilization. The resource utilization rate of the four slices under the blockchain + reinforcement learning method is all above 0.8 and the highest is 1. (5) Through the simulation test of the experiment, the results show that the average receiving throughput of video stream 1 is higher than that of video stream 2, IOT devices and mobile devices, and the average cumulative receiving throughput under the blockchain + reinforcement learning method. The highest is 1450 kbps. The average QOE of video stream 1 is higher than that of video stream 2, IOT devices and mobile devices, and the average QOE is the highest under the blockchain + reinforcement learning method, reaching 0.83.

The reinforcement learning method for occupant behavior in building control: A review

Aiming at Distributed Permutation Flow-shop Scheduling Problems (DPFSPs), this study took the minimization of the maximum completion time of the workpieces to be processed in all production tasks as the goal, and took the multi-agent Reinforcement Learning (RL) method as the main frame of the solution model, then, combining with the NASH equilibrium theory and the RL method, it proposed a NASH Q-Learning algorithm for Distributed Flow-shop Scheduling Problem (DFSP) based on Mean Field (MF). In the RL part, this study designed a two-layer online learning mode in which the sample collection and the training improvement proceed alternately, the outer layer collects samples, when the collected samples meet the requirement of batch size, it enters to the inner layer loop, which uses the Q-learning model-free batch processing mode to proceed, and adopts neural network to approximate the value function to adapt to large-scale problems. By comparing the Average Relative Percentage Deviation (ARPD) index of the benchmark test questions, the calculation results of the proposed algorithm outperformed other similar algorithms, which proved the feasibility and efficiency of the proposed algorithm.

Lexicographic multi-objective problems, which consist of multiple conflicting subtasks with explicit priorities, are common in real-world applications. Despite the advantages of Reinforcement Learning (RL) in single tasks, extending conventional RL methods to prioritized multiple objectives remains challenging. In particular, traditional Safe RL and Multi-Objective RL (MORL) methods have difficulty enforcing priority orderings efficiently. Therefore, Lexicographic Multi-Objective RL (LMORL) methods have been developed to address these challenges. However, existing LMORL methods either rely on heuristic threshold tuning with prior knowledge or are restricted to discrete domains. To overcome these limitations, we propose Lexicographically Projected Policy Gradient RL (LPPG-RL), a novel LMORL framework which leverages sequential gradient projections to identify feasible policy update directions, thereby enabling LPPG-RL broadly compatible with all policy gradient algorithms in continuous spaces. LPPG-RL reformulates the projection step as an optimization problem, and utilizes Dykstra's projection rather than generic solvers to deliver great speedups, especially for small- to medium-scale instances. In addition, LPPG-RL introduces Subproblem Exploration (SE) to prevent gradient vanishing, accelerate convergence and enhance stability. We provide theoretical guarantees for convergence and establish a lower bound on policy improvement. Finally, through extensive experiments in a 2D navigation environment, we demonstrate the effectiveness of LPPG-RL, showing that it outperforms existing state-of-the-art continuous LMORL methods.

In the wake of the vast population of smart device users worldwide, mobile health (mHealth) technologies are hopeful to generate positive and wide influence on people's health. They are able to provide flexible, affordable and portable health guides to devise users. Current online decision-making methods for mHealth assume that the users are completely heterogeneous. They share no information among users and learn a separate policy for each user. However, data for each user is very limited in size to support the separate online learning, leading to unstable policies that contain lots of variances. Besides, we find the truth that a user may be similar with some, but not all, users, and connected users tend to have similar behaviors. In this paper, we propose a network cohesion constrained (actor-critic) Reinforcement Learning (RL) method for mHealth. The goal is to explore how to share information among similar users to better convert the limited user information into sharper learned policies. To the best of our knowledge, this is the first online actor-critic RL for mHealth and first network cohesion constrained (actor-critic) RL method in all applications. The network cohesion is important to derive effective policies. We come up with a novel method to learn the network by using the warm start trajectory, which directly reflects the users' property. The optimization of our model is difficult and very different from the general supervised learning due to the indirect observation of values. As a contribution, we propose two algorithms for the proposed online RLs. Apart from mHealth, the proposed methods can be easily applied or adapted to other health-related tasks. Extensive experiment results on the HeartSteps dataset demonstrates that in a variety of parameter settings, the proposed two methods obtain obvious improvements over the state-of-the-art methods.

Deep reinforcement learning based energy management for a hybrid electric vehicle

The field of autonomous driving has seen increasing proposed use of machine learning methodologies. However, there are still challenges in applying such methods since autonomous driving involves complex and dynamic interactions with the environment. Supervised learning algorithms such as imitation learning can work in environments represented in the training data set, however, it is impractical or cost-prohibitive to collect data for all possible environments. Reinforcement learning methods can train the agent through trial and error, but it may still fail in new environments. To overcome these shortcomings, we thus propose a meta reinforcement learning (MRL) method to improve the agent's generalization capabilities to new environments. The method is applied to automated lane-changing maneuvers at different traffic congestion levels. Specifically, we train the model at light to moderate traffic conditions under a reinforcement learning framework, and then test it at heavy traffic conditions that are never encountered during training. For performance evaluation, we use both collision rate and success rate of the lane-change maneuvers to quantify the safety and effectiveness of the proposed model. A pretrained model is established as a benchmark, which uses the same network structure and training tasks as our proposed model for fair comparison. Simulation results show that the proposed method achieves an overall success rate up to 20% higher than the benchmark model when it is generalized to the new environment of heavy traffic density. The collision rate is also reduced by up to 18% compared with the benchmark model. Furthermore, the proposed model shows more stable and efficient adaptation capabilities and can achieve 100% successful rate and 0% collision rate with only a few steps of gradient update adaptation.

<p>The motivation of this thesis is the study of numerical methods for solving dynamic programming problems. In the first chapter, I present methods for reducing the computational cost imposed by the curse of dimensionality in the action and state space that occurs when solving for a Markov perfect equilibrium (MPE). These methods circumvent the computational problems for Markov perfect models in which the size of the state space or action space is large. This is because these methods are able to overcome the issue with approximating a highly non-linear or even discontinuous value function and thus allow the algorithm to use a small subset of the state space to approximate the rest of the value function. I use a model from the dynamic IO literature which is a dynamic oligopoly model with heterogeneous firms to evaluate the difference between using multidimensional Chebyshev polynomials and using artificial neural nets (ANN) for approximation, and present issues that arise when trying to use the gradient of the value function for approximations with Hermite interpolation. I also discuss how value function approximation with continuous functions can be used to find the optimal action quickly through the use of gradient based optimization techniques.</p> <p>In the second chapter I examine the use of reinforcement learning to solve a high dimensional operations research problem. This methodology expands upon the value function approximation used in the first chapter through the use of an algorithm that uses both a value function approximation and a policy function approximation. I focus on the traveling salesman problem (TSP) and train recurrent neural networks (RNN) that, given a set of city coordinates, output a probability distribution over the next city to visit in a route. Using route labels provided by Google’s OR-Tools TSP solver I train multiple network architectures using supervised learning. I compare the performance of these architectures to the performance when using the route length as a reward signal to train the networks using reinforcement learning. I show that supervised learning is a useful tool for the optimization of hyperparameters that will be used in reinforcement learning, and to evaluate the performance improvement of an architecture change. I also provide evidence that while reinforcement learning is a more general optimization framework than using handcrafted heuristics, in practice it is necessary to build a neural network architecture specific to the problem of interest and that a network architectures ability to be trained using supervised learning does not guarantee the ability to be trained using reinforcement learning.</p>

We study the approximate dynamic programming approach to revenue management in the context of attended home delivery. We draw on results from dynamic programming theory for Markov decision problems, convex optimisation and discrete convex analysis to show that the underlying dynamic programming operator has a unique fixed point. Moreover, we also show that - under certain assumptions - for all time steps in the dynamic program, the value function admits a continuous extension, which is a finite-valued, concave function of its state variables. This result opens the road for achieving scalable implementations of the proposed formulation, as it allows making informed choices of basis functions in an approximate dynamic programming context. We illustrate our findings using a simple numerical example and conclude with suggestions on how our results can be exploited in future work to obtain closer approximations of the value function.

Reinforcement Learning (RL) methods are very hopeful because they can learn useful behavior based on rewards from environment by trial and error. This paper tackles more difficult problems than the ones tackled by many ordinary RL methods: RL in POMDP (Partially Observable Markov Decision Process) environments with multiple rewards.

This paper presents a novel approach for acquiring dynamic whole-body movements on humanoid robots focused on learning a control policy for the center of mass (CoM). In our approach, we combine both a model-based CoM controller and a model-free reinforcement learning (RL) method to acquire dynamic whole-body movements in humanoid robots. (i) To cope with high dimensionality, we use a model-based CoM controller as a basic controller that derives joint angular velocities from the desired CoM velocity. The balancing issue can also be considered in the controller. (ii) The RL method is used to acquire a controller that generates the desired CoM velocity based on the current state. To demonstrate the effectiveness of our approach, we apply it to a ball-punching task on a simulated humanoid robot model. The acquired whole-body punching movement was also demonstrated on Fujitsu's Hoap-2 humanoid robot.