Optimistic MLE: A Generic Model-Based Algorithm for Partially Observable Sequential Decision Making

We consider the problem of learning monotone Boolean functions over {0, 1}/sup n/ under the uniform distribution. Specifically, given a polynomial number of uniform random samples for an unknown monotone Boolean function f, and given polynomial completing time, we would like to approximate f as well as possible. We describe a simple algorithm that we prove achieves error at most 1/2-/spl Omega/(1//spl radic/n), improving on the previous best bound of 1/2-/spl Omega/((log/sup 2/ n)/n). We also prove that no algorithm, given a polynomial number of samples, can guarantee error 1/2-/spl omega/((log n)//spl radic/n), improving on the previous best hardness bound of O(1//spl radic/n). These lower bounds hold even if the learning algorithm is allowed membership queries. Thus this paper settles to an O(log n) factor the question of the best achievable error for learning the class of monotone Boolean functions with respect to the uniform distribution.

Robots had a great impact on the manufacturing industry ever since the early seventies when companies such as KUKA and ABB started deploying their first industrial robots. These robots merely performed very specific tasks in specific ways within well-defined environments. Still, they proved to be very useful as they could exceed human performance at these tasks. However, in order to enable robots to enter our daily life, they need to become more versatile and need to operate in much less structured environments. This thesis is partly devoted to stretching these limitations by means of learning, namely imitation learning (IL) and inverse reinforcement learning (IRL). Reinforcement learning (RL) is a powerful approach to enable robots to solve a task in an unknown environment. The practitioner describes a desired behavior by specifying a reward function and the robot autonomously interacts with the environment in order to find a control policy that generates high accumulated reward. However, RL is not suitable for teaching new tasks by non-experts because specifying appropriate reward functions can be difficult. Demonstrating the desired behavior is often easier for non-experts. Imitation learning can be used in order to enable the robot to reproduce the demonstrations. However, without explicitly inferring and modeling the intentions of the demonstrations, it can become difficult to solve the task for unseen situations. Inverse reinforcement learning (IRL) therefore aims to infer a reward function from the demonstrations, such that optimizing this reward function yields the desired behavior even for different situations. This thesis introduces a unifying approach to solve the inverse reinforcement learning problem in the same way as the reinforcement learning problem. This is achieved by framing both problems as information projection problems, i.e., we strive to minimize the relative entropy between a probabilistic model of the robot behavior and a given desired distribution. Furthermore, a trust region on the robot behavior is used to stabilize the optimization. For inverse reinforcement learning, the desired distribution is implicitly given by the expert demonstrations. The resulting optimization can be efficiently solved using state-of-the-art reinforcement learning methods. For reinforcement learning, the log-likelihood of the desired distribution is given by the reward function. The resulting optimization problem corresponds to a standard reinforcement learning formulation, except for an additional objective of maximizing the entropy of the robot behavior. This entropy objective adds little overhead to the optimization, but can lead to better exploration and more diversified policies. Trust-region I-projections are not only useful for training robots, but can also be applied to other machine learning problems. I-projections are typically used for variational inference, in order to approximate an intractable distribution by a simpler model. However, the resulting optimization problems are usually optimized based on stochastic gradient descent which often suffers from high variance in the gradient estimates. As trust-region I-projections where shown to be effective for reinforcement learning and inverse reinforcement learning, this thesis also explores their use for variational inference. More specifically, trust-region I-projections are investigated for the problem of approximating an intractable distribution by a Gaussian mixture model (GMM) with an adaptive number of components. GMMs are highly desirable for variational inference because they can yield arbitrary accurate approximations while inference from GMMs is still relatively cheap. In order to make learning the GMM feasible, we derive a lower bound that enables us to decompose the objective function. The optimization can then be performed by iteratively updating individual components using a technique from reinforcement learning. The resulting method is capable of learning approximations of significantly higher quality than existing variational inference methods. Due to the similarity of the underlying optimization problems, the insights gained from our variational inference method are also useful for IL and IRL. Namely, a similar lower bound can be applied also for the I-projection formulation of imitation learning. However, whereas for variational inference the lower bound serves to decompose the objective function, for imitation learning it allows us to provide a reward signal to the robot that does not depend on its behavior. Compared to reward functions that are relative to the current behavior of the robot---which are typical for popular adversarial methods---behavior-independent reward functions have the advantages that we can show convergence even for greedy optimization. Furthermore, behavior-independent reward functions solve the inverse reinforcement learning problem, thereby closing the gap between imitation learning and IRL. However, algorithms derived from our non-adversarial formulation are actually very similar to existing AIL methods, and we can even show that adversarial inverse reinforcement learning (AIRL) is indeed an instance of our formulation. AIRL was derived from an adversarial formulation, and we point out several problems of that derivation. In contrast, we show that AIRL can be straightforwardly derived from out non-adversarial formulation. Furthermore, we demonstrate that the non-adversarial formulation can be also used to derive novel algorithms by presenting a non-adversarial method for offline imitation learning.

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.

Approximation biases of value functions are considered a key problem in reinforcement learning (RL). In particular, existing RL algorithms are hindered by overestimation and underestimation biases, i.e., value mismatching between RL's actual returns and action-value approximations limits the performance of RL algorithms. In this article, we first develop a new synthesis loss function for RL's action-value estimation integrating a regularization term and a modified "clipped double Q-learning" structure for solving overestimation and underestimation biases. To minimize the differences between action-value estimations and actual returns in RL, we develop a new discrepancy function to determine the type and magnitude of approximation biases. Then, two coefficients embedded in the synthesis loss are automatically tuned by minimizing the discrepancy function during training to minimize approximation biases. We further design a new actor-critic (AC) algorithm, named AC with synthesis loss (ACSL), by integrating the synthesis loss function and an error-controlled mechanism. Experimental results on continuous control tasks illustrate that the proposed ACSL algorithm outperforms other cutting-edge RL methods in many tasks and that the proposed synthesis loss function is easily implemented into other algorithms and significantly reduces approximation biases while improving performance. The proposed method can successfully handle many complex continuous control tasks and can greatly outperform other state-of-the-art algorithms on most tasks.

We consider the exploration/exploitation problem in reinforcement learning (RL). The Bayesian approach to model-based RL offers an elegant solution to this problem, by considering a distribution over possible models and acting to maximize expected reward; unfortunately, the Bayesian solution is intractable for all but very restricted cases. In this paper we present a simple algorithm, and prove that with high probability it is able to perform e-close to the true (intractable) optimal Bayesian policy after some small (polynomial in quantities describing the system) number of time steps. The algorithm and analysis are motivated by the so-called PAC-MDP approach, and extend such results into the setting of Bayesian RL. In this setting, we show that we can achieve lower sample complexity bounds than existing algorithms, while using an exploration strategy that is much greedier than the (extremely cautious) exploration of PAC-MDP algorithms.

Nonlinear system control using self-evolving neural fuzzy inference networks with reinforcement evolutionary learning

We investigate the convergence properties of policy iteration and value iteration algorithms in reinforcement learning by leveraging fixed-point theory, with a focus on mappings that exhibit weak contractive behavior. Unlike traditional studies that rely on strong contraction properties, such as those defined by the Banach contraction principle, we consider a more general class of mappings that includes weak contractions. Employing Zamfirscu’s fixed-point theorem, we establish sufficient conditions for norm convergence in infinite-dimensional policy spaces under broad assumptions. Our approach extends the applicability of these algorithms to feedback control problems in reinforcement learning, where standard contraction conditions may not hold. Through illustrative examples, we demonstrate that this framework encompasses a wider range of operators, offering new insights into the robustness and flexibility of iterative methods in dynamic programming.

In Reinforcement Learning, an intelligent agent has to make a sequence of decisions to accomplish a goal. If this sequence is long, then the agent has to plan over a long horizon. While learning the optimal policy and its value function is a well studied problem in Reinforcement Learning, this paper focuses on the structure of the optimal value function and how hard it is to represent the optimal value function. We show that the generalized Rademacher complexity of the hypothesis space of all optimal value functions is dependent on the planning horizon and independent of the state and action space size. Further, we present bounds on the action-gaps of action value functions and show that they can collapse if a long planning horizon is used. The theoretical results are verified empirically on randomly generated MDPs and on a grid-world fruit collection task using deep value function approximation. Our theoretical results highlight a connection between value function approximation and the Options framework and suggest that value functions should be decomposed along bottlenecks of the MDP's transition dynamics.

One of the important problems in reinforcement learning is the problem of incomplete perception, i.e., how to select the optimal action when the perception of the learning agent is not sufficient in detecting the states of the environment. One of the proposed solutions to this problem is to utilize recurrent neural networks for the architecture of the learning agent to build an internal dynamic model of the environment and to take actions based on the states of the model. Another approach is the stochastic gradient ascent method (SGA), proposed by Kimura et al. (1996), as a learning method for this problem. However, the SGA, which selects actions based on immediate percepts, can only achieve suboptimal performance under incomplete perception. This paper studies a combination of these techniques, where SGA is applied to recurrent neural networks. Computer simulations show that a learning agent using the proposed method can achieve optimal performance under incomplete perception.

Over the last few decades, an open-loop control method known as input shaping has shown to be effective in minimizing unwanted residual vibration of flexible machines. Traditionally, an input shaper is created through either a direct solution of a set of equations describing the system response or through an optimization problem addressing those equations. This paper introduces a new way to design an input shaper using a machine learning approach. It also proposes some changes to a traditional machine learning algorithm as an alternative solution for one of the most fundamental problems in reinforcement learning known as the exploration-exploitation dilemma. This paper serves as a foundation for a new class of input shapers designed by machine learning that could potentially be developed into a wide-ranging adaptive control solution.

This paper focuses on the development of a learning-based heuristic for the machine scheduling problem, which automatically captures the search control knowledge or the common features of good schedules while generating a number of schedules. Defining states and actions of the machine shop, the machine scheduling problem is transformed into a problem of reinforcement learning (RL) in which a learner or a scheduler will learn to select the right action at each state of the machine shop, using the reward from a schedule evaluator for executing the action. Implementing the proposed reinforcement learning with a genetic algorithm results in the genetic reinforcement learning (GRL) approach to the machine scheduling problem. Although the learning-based heuristic has the overhead of acquiring knowledge on the problem, it can be easily adapted for a wide variety of machine scheduling problems due to the weak dependence on the problem structures and objectives. A GRL-based scheduler, called EVIS (Evolutionary Intracell Scheduler), has been developed and applied to various classes of machine scheduling problems, such as the job-shop scheduling, the flow-shop scheduling and the open-shop scheduling problems, and even the processor scheduling problem, the performance evaluation of EVIS with a number of different problem instances has shown that the learning-based heuristic is robust and its performance is comparable with that of other problem-specific heuristics or search-oriented heuristics in the quality of solutions.

Sample efficiency is a crucial problem in Reinforcement Learning, especially when tackling environments with sparse reward signals that make convergence and learning cumbersome. In this work, a novel method is developed that combines Rapidly Exploring Random Trees with Reinforcement Learning to mitigate the inefficiency of the trial-and-error-based experience-gathering concept through the systematic exploration of the state space. The combined approach eliminates the redundancy in irrelevant training samples. Consequently, the pivotal training signals, despite their sparsity, can be further exposed to support the learning process. Experiments are made on several OpenAI gym environments to demonstrate that the proposed method does not have any context-dependent components, and the results show that it can outperform the classic trial-and-error-based training approach.

Space-air-ground integrated networks (SAGIN) have been envisioned as the promising and key network architecture for the 6G vehicular networks to provide seamless coverage for the connected vehicles. To access the most appropriate network quickly, this paper proposed a knowledge-driven network access approach, where the communication knowledge is explicitly integrated into neural networks, to deal with multiple tasks in SAGIN-based vehicular networks. Specifically, the formulated long-term network access problem is handled by asynchronous advantage actor-critic algorithm (A3C) in reinforcement learning. During this process, the space-time correlation knowledge is introduced to effectively reduce the action space in channel selection and the reward shaping exploiting the problem-specific communication and mathematical knowledge is adopted to solve the sparse reward problem in reinforcement learning. In addition, by modifying the sub-net learning rate of the A3C algorithm with experimental experience, this paper speeds up the network convergence speed by 1.5%. Numerical results also show that integrating knowledge into traditional deep reinforcement learning algorithm can improve the reward by 4%.

Exploration is a challenging problem in reinforcement learning (RL), especially in environments with sparse rewards.Quantifying and utilizing the parametric uncertainty has been shown to be paramount for successful exploration [Osband et al., 2018].Bayesian, or approximately Bayesian, methods present a principled means of estimating the parametric uncertainty in RL problems.Gaussian processes, nonparametric Bayesian models, are often impractical due to poor scalability and computational bottlenecks.We introduce a scalable Gaussian process RL (GPRL) method which directly induces sparsity in the covariance matrix to facilitate faster computation.This is a departure from previous GPRL methods which instead rely on data reduction and subsampling.We compare various covariance-based exploration techniques (Thompson sampling, upper confidence bound, and probabilistic maximum variance) which leverage our scalable GP framework in sparse reward environments.Finally, we show favorable comparison against the bootstrapped deep Q-Network.

Empirical tests indicate that at least one class of genetic algorithms yields good performance for neural network weight optimization in terms of learning rates and scalability. The successful application of these genetic algorithms to supervised learning problems sets the stage for the use of genetic algorithms in reinforcement learning problems. On a simulated inverted-pendulum control problem, “genetic reinforcement learning” produces competitive results with AHC, another well-known reinforcement learning paradigm for neural networks that employs the temporal difference method. These algorithms are compared in terms of learning rates, performance-based generalization, and control behavior over time.