Reward-predictive representations generalize across tasks in reinforcement learning

This presentation is about our AAMAS 2020 paper ""Plannable Approximations to MDP Homomorphisms: Equivariance under Actions"". This work exploits action equivariance for representation learning in reinforcement learning. Equivariance under actions states that transitions in the input space are mirrored by equivalent transitions in latent space, while the map and transition functions should also commute. We introduce a contrastive loss function that enforces action equivariance on the learned representations. We prove that when our loss is zero, we have a homomorphism of a deterministic Markov Decision Process (MDP). Learning equivariant maps leads to structured latent spaces, allowing us to build a model on which we plan through value iteration. We show experimentally that for deterministic MDPs, the optimal policy in the abstract MDP can be successfully lifted to the original MDP. Moreover, the approach easily adapts to changes in the goal states. Empirically, we show that in such MDPs, we obtain better representations in fewer epochs compared to representation learning approaches using reconstructions, while generalizing better to new goals than model-free approaches.

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.

Reinforcement Learning (RL) Markov Decision Processes is studied with an emphasis on the well-studied exploration problem. We first formulate and discuss a definition of “efficient” algorithms that is termed Probably Approximately Correct (PAC) in RL. Next we provide general sufficient conditions for such an algorithm that applies to several different modeling assumptions. The conditions can be used to demonstrate that efficient learning is possible in finite MDPs, with either a model-based or model-free approach, in factored MDPs, and in continuous MDPs with linear dynamics. In the reinforcement-learning (RL) problem (Sutton & Barto 1998), an agent acts in an unknown or incompletely known environment with the goal of maximizing an external reward signal. In the most standard mathematical formulation of the problem, the environment is modeled as a Markov Decision Process (MDP) and the goal of the agent is to obtain near-optimal discounted return. Over the years, many algorithms have been proposed for this problem, but analyses of their performances have been relatively scarce. In fact, until recently, most theoretical guarantees have been that certain algorithms will discover an optimal policy in the limit, after an infinite amount of experience. In contrast, several attempts have been made to study “Probably Approximately Correct” or PAC-MDP algorithms, which exhibit near-optimal behavior in polynomial time and experience. This paper discusses several extensions of those results. We present a theorem that provides sufficient conditions for an algorithm to be PAC-MDP. We examine these conditions and show how they can be applied to prove that efficient learning is possible in three interesting scenerios: finite MDPs (i.e. the “Tabular case”),

Reinforcement learning (RL) agents often fail in adversarial environments where the Markov Decision Process (MDP) assumption of a stationary environment is violated. While model-free solutions for this setting exist, planning-based counterparts remain less explored. This paper introduces offline and online value iteration algorithms within the Threatened Markov Decision Process (TMDP) framework, in which the RL agent maintains and updates a Bayesian belief over the adversary’s policy. The belief is integrated into a modified Bellman optimality equation to compute robust policies. We evaluate our framework with the stochastic adversarial multi-agent Coin Game. Our primary finding is that the model-based agent outperforms the TMDP version of model-free Q-learning by a significant margin, confirming that the benefits of model-based planning extend from MDP to TMDP. Furthermore, the proposed framework maintains a performance advantage over Q-learning baselines even when the system’s transition function is unknown. The RL agent also demonstrated robustness to direct adversarial interactions. This work validates TMDP value iteration as an effective, planning-based approach for decision-making against adaptive adversaries.

Advanced planning for autonomous vehicles using reinforcement learning and deep inverse reinforcement learning

The theme of my feature article is the crossfertilization of ideas from artificial intelligence and operations research, although it is important to emphasize that some of the key ideas of approximate dynamic programming also draw heavily on developments whose origins should be attributed to control theory. I am very grateful for the insightful remarks of John N. Tsitsiklis, well known for his many contributions to approximate dynamic programming and his coauthorship of a seminal book (Bertsekas and Tsitsiklis 1996), and Andrzej Ruszczynski, one of the very top names in the field of stochastic programming who, in addition to numerous research papers, coedited the volume on stochastic programming in the prestigious Handbook on Operations Research and Management Science series (Ruszczynski and Shapiro 2003). I also benefited from extensive comments by Andy Barto who, with Richard Sutton, coauthored the book Reinforcement Learning, which is the bible of this hugely popular field (Sutton and Barto 1998). Both sets of comments add a number of useful insights. I am going to focus my final remarks less on the specifics of their remarks and more on the differences in perspectives they bring from their home communities. I also need to note that there is no such thing as the “operations research perspective”— rather, there are at least four major subcommunities within operations research that deal directly with stochastic optimization: Markov decision processes (MDPs) (as represented by Puterman 1994), stochastic programming (Kall and Wallace 1994, Higle and Sen 1996, and Birge and Louveaux 1997 are major references), decision theory (primarily decision trees, as in Skinner 1999), and simulation-optimization (see, for example, Swisher et al. 2000, Fu 2002). Tsitsiklis (2010) notes the strong similarities between operations research and the field of systems and control theory. In drawing on this conclusion, he is focusing on the central paradigm of optimizing a known objective function with known system dynamics. Artificial intelligence (AI), by contrast, is often addressing the problem of learning how people behave (or more fundamentally, how the brain solves problems), often in the context of applications where we may not understand why someone is making a particular decision (hence, we may not know the reward function). Also, these applications often take place in an online setting where we are observing events from an external, physical system. As a result, we may be able to observe the next state we land in, but we do not necessarily know the physics of why we landed there. The first difference someone will notice between these communities appears purely cosmetic. The AI and MDP communities use state s and action a; elsewhere, operations research will typically use x for a decision, expecting it to be a high-dimensional vector. In control theory, the state is x and the decision (control) is u. Behind these cosmetic differences are problem classes with associated empirical properties and computational expectations. A 10-dimensional control problem can be much harder than an OR problem with 10,000 dimensions. A second and significant difference between the communities is how they represent the dynamics of the system. In the MDP community, it is absolutely routine to start by knowing the transition matrix p s′ s x , which gives the probability of landing in (typically discrete) state s′, given that we are in state s and take action x. However, there are many problems where this matrix is either simply unknown or computationally intractable (for example, if the number of states is too large). Computing the transition matrix requires first knowing the transition function, which might be written as (using my notation)

Feature Reinforcement Learning: Part I. Unstructured MDPsGeneral-purpose, intelligent, learning agents cycle through sequences of observations, actions, and rewards that are complex, uncertain, unknown, and non-Markovian. On the other hand, reinforcement learning is well-developed for small finite state Markov decision processes (MDPs). Up to now, extracting the right state representations out of bare observations, that is, reducing the general agent setup to the MDP framework, is an art that involves significant effort by designers. The primary goal of this work is to automate the reduction process and thereby significantly expand the scope of many existing reinforcement learning algorithms and the agents that employ them. Before we can think of mechanizing this search for suitable MDPs, we need a formal objective criterion. The main contribution of this article is to develop such a criterion. I also integrate the various parts into one learning algorithm. Extensions to more realistic dynamic Bayesian networks are developed in Part II (Hutter, 2009c). The role of POMDPs is also considered there.

We study the sample complexity of offline learning for a class of structured Markov decision processes (MDPs) describing the inventory control system with fixed ordering cost/setup cost, a fundamental problem in supply chains. We find that a naive plug-in sampling-based approach applied to the inventory MDPs leads to strictly lower sample complexity bounds compared to the optimal bounds recently obtained for the general MDPs. More specifically, in the infinite-horizon discounted cost setting, we obtain an O ~ ( min { ( S ¯ − s _ ) 2 ( 1 − γ ) 2 ϵ 2 , 1 ( 1 − γ ) 4 ϵ 2 } ) sample complexity bound, where ( S ¯ − s _ ) 2 corresponds to the number of state-action pairs in a generic MDP with state space S and action space A . As such, O ~ ( ( S ¯ − s _ ) 2 ( 1 − γ ) 2 ϵ 2 ) improves on the optimal generic reinforcement learning (RL) bound Θ ~ ( ( S ¯ − s _ ) 2 ( 1 − γ ) 3 ϵ 2 ) (when directly applying Θ ~ ( | S | | A | ( 1 − γ ) 3 ϵ 2 ) here) by a factor of ( 1 − γ ) − 1 , and O ~ ( 1 ( 1 − γ ) 4 ϵ 2 ) is able to completely remove the dependence on state and action cardinality. In the infinite-horizon average cost setting, we obtain an O ~ ( ( S ¯ − s _ ) 2 ϵ 2 ) bound, improving on the generic optimal RL bound Θ ~ ( ( S ¯ − s _ ) 2 t m i x ϵ 2 ) (when directly applying Θ ~ ( | S | | A | t m i x ϵ 2 ) here) by a factor of t m i x , and hence removing the mixing time dependence. By carefully leveraging the structural properties of the inventory dynamics in various settings, we are able to improve on those “best-possible” bounds developed in the RL literature. Our results demonstrate the drawbacks one could face by blindly following RL algorithms and the necessity of designing sample efficient algorithms that properly incorporate the special structures of the inventory systems.

Recently, it was demonstrated that the design synthesis of truss structures can be modeled as a Markov decision process (MDP) and solved using a tabular reinforcement learning method. In this setting, each state corresponds to a specific design configuration represented as a finite graph. However, when the structural design domain is relatively large, and depending on the constraints, the dimensionality of the state space becomes quite large rendering tabular reinforcement learning algorithms inefficient. Hence, in this study, the design synthesis MDP framework is significantly extended to solve structural design problems with large state spaces, by integrating deep reinforcement learning (DRL) into the general MDP framework. This is beneficial because with DRL, a deep neural network can be used to approximate the state-action value function, such that the network has much fewer parameters than the cardinality of the state space. This parameterization relies upon a problem relevant set of features and reward function. Thus, for this extended DRL design synthesis (DRLDS) framework, a compact set of features and a reward function are devised that are suitable for structural design problems where structural configurations are represented as finite graphs. Through the application of seven different structural design synthesis examples, the DRLDS framework is demonstrated to be capable of adeptly learning optimal policies that synthesize high, if not the highest, performing design solutions more frequently. The DRLDS framework does this with fewer finite element model evaluations than other considered alternative methods, further demonstrating the effectiveness of the developed set of features and reward function.

Reinforcement Learning (RL) is a machine learning methodology that develops the capability to make sequential decisions in intricate issues using trial-and-error techniques. RL has become increasingly prevalent for decision-making and control tasks in diverse fields such as industrial processes, biochemical systems and energy management. This review paper presents a comprehensive examination of the development, models, algorithms and practical uses of RL, with a specific emphasis on its application in process control. The study examines the fundamental theories, methodology and applications of RL, classifying them into two categories: classical RL such as such as Markov decision processes (MDP) and deep RL viz., actor critic methods. RL is a topic of discussion in multiple process industries, such as industrial chemical process control, biochemical process control, energy systems, wastewater treatment and the oil and gas sector. Nevertheless, the paper also highlights challenges that hinder its larger acceptance, including the requirement for substantial computational resources, the complexity of simulating real-world settings and the challenge of guaranteeing the stability and resilience of RL algorithms in dynamic and unpredictable environments. RL has demonstrated significant promise, but more research is needed to fully integrate it into industrial and environmental systems in order to solve the current challenges. Abbreviations: AC: Actor critic; AI: Artificial intelligence; ANN: Artificial neural networks; A3C: Asynchronous advantage actor critic; CRL : Classical Reinforcement learning; CV : Controlled variable; DDPG : Deep deterministic policy gradient; DQN: Deep Q network; DRL: Deep reinforcement learning; DP: Dynamic programming; FOMDP: Fully observable Markov decision process; GRU: Gated recurrent unit; LQR: Linear quadratic regulator; LSTM: Long short-term memory; ML: Machine learning; MV : Manipulated variable; MC: Monte Carlo; MDP: Markov decision process; MPC: Model predictive controller; MIMO: Multi input multi output; PG: Policy gradient; PID: Proportional integral derivative; PPO: Proximal policy optimisation; RL: Reinforcement learning; PPO: Proximal policy optimisation; SAC: Soft actor critic; SISO: Single input single output; TD: Temporal difference; TRPO: Trust region policy optimisation; TD3: Twin delayed deep deterministic policy gradient.

This paper proposes a novel and practical model-based learning approach with iterative refinement for solving continuous (and hybrid) Markov decision processes. Initially, an approximate model is learned using conventional sampling methods and solved to obtain a policy. Iteratively, the approximate model is refined using variance in the utility values as partition criterion. In the learning phase, initial reward and transition functions are obtained by sampling the state-action space. The samples are used to induce a decision tree predicting reward values from which an initial partition of the state space is built. The samples are also used to induce a factored MDP. The state abstraction is then refined by splitting states only where the split is locally important. The main contributions of this paper are the use of sampling to construct an abstraction, and a local refinement process of the state abstraction based on utility variance. The proposed technique was tested in AsistO, an intelligent recommender system for power plant operation, where we solved two versions of a complex hybrid continuous-discrete problem. We show how our technique approximates a solution even in cases where standard methods explode computationally

In this paper, We consider an uncertain Markov decision process (MDP) with a control cost and a linear temporal logic (LTL) control specification. We propose a reinforcement learning (RL) based method for design of an optimal control policy by which the controlled MDP satisfies the control specification with probability 1 and minimizes an expected discounted sum of the control costs. First, we construct a deterministic Rabin automaton (DRA) that accepts all and only infinite words satisfying the LTL control specification. Second, we construct a product MDP of the MDP and the DRA to represent a dynamic control policy that satisfies the control specification. Third, we modify the product MDP in order to apply RL to the design of an optimal control policy. The control action of the modified product MDP is a pair of a pattern and an action, where the pattern is a set of actions. Moreover, we introduce a reward that represents both the satisfaction of the control specification and the minimally restrictiveness of the pattern. Finally, we proposed an algorithm for design of an optimal control policy that consists of a sequential decision making of two steps. At the first decision making, we select a pattern that maximizes a discounted sum of the reward. At the second one, we select an action from the pattern selected at the first one such that it minimizes the expected discounted sum of the costs. Moreover, we consider an illustrative example to show that the proposed algorithm can obtain an optimal control policy.

This paper proposes a demand response method to reduce the long-term charging cost of single plug-in electric vehicles (PEV) while overcoming obstacles such as the stochastic nature of the user's driving behaviour, traffic condition, energy usage, and energy price. The problem is formulated as a Markov Decision Process (MDP) with an unknown transition probability matrix and solved using deep reinforcement learning (RL) techniques. The proposed method does not require any initial data on the PEV driver's behaviour and shows improvement on learning speed when compared to a pure model-free reinforcement learning method. A combination of model-based and model-free learning methods called Dyna-Q reinforcement learning is utilized in our strategy. Every time a real experience is obtained, the model is updated, and the RL agent will learn from both the real experience and “imagined” experiences from the model. Due to the vast amount of state space, a table-lookup method is impractical, and a value approximation method using deep neural networks is employed for estimating the long-term expected reward of all state-action pairs. An average of historical price and a long short-term memory (LSTM) network are used to predict future price. Simulation results demonstrate the effectiveness of this approach and its ability to reach an optimal policy quicker while avoiding state of charge (SOC) depletion during trips when compared to existing PEV charging schemes.

Reinforcement learning (RL) is one of the popular methods for intelligent control and decision making in the field of robotics recently. The goal of RL is to learn an optimal policy of the agent by interacting with the environment via trail and error. There are two main algorithms for RL problems, including model-free and model-based methods. Model-free RL is driven by historical trajectories and empirical data of the agent to optimize the policy, which needs to take actions in the environment to collect the trajectory data and may cause the damage of the robot during training in the real environment. The main different between model-based and model-free RL is that a model of the transition probability in the interaction environment is employed. Thus the agent can search the optimal policy through internal simulation. However, the model of the transition probability is usually estimated from historical data in a single environment with statistical errors. Therefore, an issue is faced by the agent is that the optimal policy is sensitive to perturbations in the model of the environment which can lead to serious degradation in performance. Robust RL aims to learn a robust optimal policy that accounts for model uncertainty of the transition probability to systematically mitigate the sensitivity of the optimal policy in perturbed environments. In this overview, we begin with an introduction to the algorithms in RL, then focus on the model uncertainty of the transition probability in robust RL. In parallel, we highlight the current research and challenges of robust RL for robot control. To conclude, we describe some research areas in robust RL and look ahead to the future work about robot control in complex environments.

Explainable reinforcement learning (XRL) is an emerging subfield of explainable machine learning that has attracted considerable attention in recent years. The goal of XRL is to elucidate the decision-making process of reinforcement learning (RL) agents in sequential decision-making settings. Equipped with this information, practitioners can better understand important questions about RL agents (especially those deployed in the real world), such as what the agents will do and why. Despite increased interest, there exists a gap in the literature for organizing the plethora of papers—especially in a way that centers the sequential decision-making nature of the problem. In this survey, we propose a novel taxonomy for organizing the XRL literature that prioritizes the RL setting. We propose three high-level categories: feature importance, learning process and Markov decision process, and policy-level. We overview techniques according to this taxonomy, highlighting challenges and opportunities for future work. We conclude by using these gaps to motivate and outline a roadmap for future work.