Making the right decision in traffic is a challenging task that is highly dependent on individual preferences as well as the surrounding environment. Therefore it is hard to model solely based on expert knowledge. In this work we use Deep Reinforcement Learning to learn maneuver decisions based on a compact semantic state representation. This ensures a consistent model of the environment across scenarios as well as a behavior adaptation function, enabling on-line changes of desired behaviors without re-training. The input for the neural network is a simulated object list similar to that of Radar or Lidar sensors, superimposed by a relational semantic scene description. The state as well as the reward are extended by a behavior adaptation function and a parameterization respectively. With little expert knowledge and a set of mid-level actions, it can be seen that the agent is capable to adhere to traffic rules and learns to drive safely in a variety of situations.
Since it can be problematic to model multi-agent scenarios as a Markov Decision Process (MDP) due to the unpredictable behavior of other agents, one possibility is to decompose the problem into learning a cost function for driving trajectories @cite_12 . To make learning faster and more data efficient, expert knowledge can be incorporated by restricting certain actions during the training process @cite_22 . Additionally, there is the option to handle task and motion planning by learning low-level controls for lateral as well as longitudinal maneuvers from a predefined set and a high-level maneuver policy @cite_0 .
@cite_0 @cite_22 @cite_12
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This thesis addresses the question of planning under uncertainty within a time-dependent changing environment. Original motivation for this work came from the problem of building an autonomous agent able to coordinate with its uncertain environment; this environment being composed of other agents communicating their intentions or non-controllable processes for which some discrete-event model is available. We investigate several approaches for modeling continuous time-dependency in the framework of Markov Decision Processes (MDPs), leading us to a definition of Temporal Markov Decision Problems. Then our approach focuses on two separate paradigms. First, we investigate time-dependent problems as processes and describe them through the formalism of Time-dependent MDPs (TMDPs). We extend the existing results concerning optimality equations and present a new Value Iteration algorithm based on piecewise polynomial function representations in order to solve a more general class of TMDPs. This paves the way to a more general discussion on parametric actions in hybrid state and action spaces MDPs with continuous time. In a second time, we investigate the option of separately modeling the concurrent contributions of exogenous events. This approach of modeling leads to the use of Generalized Semi-Markov Decision Processes (GSMDP). We establish a link between the general framework of Discrete Events Systems Specification (DEVS) and the formalism of GSMDP, allowing us to build sound discrete-event compatible simulators. Then we introduce a simulation-based Policy Iteration approach for explicit-event Temporal Markov Decision Problems. This algorithmic contribution brings together results from simulation theory, forward search in MDPs, and statistical learning theory. The implicit-event approach was tested on a specific version of the Mars rover planning problem and on a drone patrol mission planning problem while the explicit-event approach was evaluated on a subway network control problem. Decision making usually involves choosing among different courses of action over a broad range of time scales. For instance, a person planning a trip to a distant location makes high-level decisions regarding what means of transportation to use, but also chooses low-level actions, such as the movements for getting into a car. The problem of picking an appropriate time scale for reasoning and learning has been explored in artificial intelligence, control theory and robotics. In this dissertation we develop a framework that allows novel solutions to this problem, in the context of Markov Decision Processes (MDPs) and reinforcement learning. In this dissertation, we present a general framework for prediction, control and learning at multiple temporal scales. In this framework, temporally extended actions are represented by a way of behaving (a policy) together with a termination condition. An action represented in this way is called an option. Options can be easily incorporated in MDPs, allowing an agent to use existing controllers, heuristics for picking actions, or learned courses of action. The effects of behaving according to an option can be predicted using multi-time models, learned by interacting with the environment. In this dissertation we develop multi-time models, and we illustrate the way in which they can be used to produce plans of behavior very quickly, using classical dynamic programming or reinforcement learning techniques. The most interesting feature of our framework is that it allows an agent to work simultaneously with high-level and low-level temporal representations. The interplay of these levels can be exploited in order to learn and plan more efficiently and more accurately. We develop new algorithms that take advantage of this structure to improve the quality of plans, and to learn in parallel about the effects of many different options. Despite the significant progress to extend Markov Decision Processes (MDP) to cooperative multi-agent systems, developing approaches that can deal with realistic problems remains a serious challenge. Existing approaches that solve Decentralized Markov Decision Processes (DEC-MDPs) suffer from the fact that they can only solve relatively small problems without complex constraints on task execution. OC-DEC-MDP has been introduced to deal with large DEC-MDPs under resource and temporal constraints. However, the proposed algorithm to solve this class of DEC-MDPs has some limits: it suffers from overestimation of opportunity cost and restricts policy improvement to one sweep (or iteration). In this paper, we propose to overcome these limits by first introducing the notion of Expected Opportunity Cost to better assess the influence of a local decision of an agent on the others. We then describe an iterative version of the algorithm to incrementally improve the policies of agents leading to higher quality solutions in some settings. Experimental results are shown to support our claims. Reinforcement Learning was originally developed for Markov Decision Processes (MDPs). It allows a single agent to learn a policy that maximizes a possibly delayed reward signal in a stochastic stationary environment. It guarantees convergence to the optimal policy, provided that the agent can sufficiently experiment and the environment in which it is operating is Markovian. However, when multiple agents apply reinforcement learning in a shared environment, this might be beyond the MDP model. In such systems, the optimal policy of an agent depends not only on the environment, but on the policies of the other agents as well. These situations arise naturally in a variety of domains, such as: robotics, telecommunications, economics, distributed control, auctions, traffic light control, etc. In these domains multi-agent learning is used, either because of the complexity of the domain or because control is inherently decentralized. In such systems it is important that agents are capable of discovering good solutions to the problem at hand either by coordinating with other learners or by competing with them. This chapter focuses on the application reinforcement learning techniques in multi-agent systems. We describe a basic learning framework based on the economic research into game theory, and illustrate the additional complexity that arises in such systems. We also described a representative selection of algorithms for the different areas of multi-agent reinforcement learning research. Learning, planning, and representing knowledge at multiple levels of temporal ab- straction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforce- ment learning and Markov decision processes (MDPs). We extend the usual notion of action in this framework to include options—closed-loop policies for taking ac- tion over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as mus- cle twitches and joint torques. Overall, we show that options enable temporally abstract knowledge and action to be included in the reinforcement learning frame- work in a natural and general way. In particular, we show that options may be used interchangeably with primitive actions in planning methods such as dynamic pro- gramming and in learning methods such as Q-learning. Formally, a set of options defined over an MDP constitutes a semi-Markov decision process (SMDP), and the theory of SMDPs provides the foundation for the theory of options. However, the most interesting issues concern the interplay between the underlying MDP and the SMDP and are thus beyond SMDP theory. We present results for three such cases: 1) we show that the results of planning with options can be used during execution to interrupt options and thereby perform even better than planned, 2) we introduce new intra-option methods that are able to learn about an option from fragments of its execution, and 3) we propose a notion of subgoal that can be used to improve the options themselves. All of these results have precursors in the existing literature; the contribution of this paper is to establish them in a simpler and more general setting with fewer changes to the existing reinforcement learning framework. In particular, we show that these results can be obtained without committing to (or ruling out) any particular approach to state abstraction, hierarchy, function approximation, or the macro-utility problem. As computational learning agents move into domains that incur real costs (e.g., autonomous driving or financial investment), it will be necessary to learn good policies without numerous high-cost learning trials. One promising approach to reducing sample complexity of learning a task is knowledge transfer from humans to agents. Ideally, methods of transfer should be accessible to anyone with task knowledge, regardless of that person's expertise in programming and AI. This paper focuses on allowing a human trainer to interactively shape an agent's policy via reinforcement signals. Specifically, the paper introduces "Training an Agent Manually via Evaluative Reinforcement," or TAMER , a framework that enables such shaping. Differing from previous approaches to interactive shaping, a TAMER agent models the human's reinforcement and exploits its model by choosing actions expected to be most highly reinforced. Results from two domains demonstrate that lay users can train TAMER agents without defining an environmental reward function (as in an MDP) and indicate that human training within the TAMER framework can reduce sample complexity over autonomous learning algorithms. Consider a multi-agent system in a dynamic and uncertain environment. Each agent's local decision problem is modeled as a Markov decision process (MDP) and agents must coordinate on a joint action in each period, which provides a reward to each agent and causes local state transitions. A social planner knows the model of every agent's MDP and wants to implement the optimal joint policy, but agents are self-interested and have private local state. We provide an incentive-compatible mechanism for eliciting state information that achieves the optimal joint plan in a Markov perfect equilibrium of the induced stochastic game. In the special case in which local problems are Markov chains and agents compete to take a single action in each period, we leverage Gittins allocation indices to provide an efficient factored algorithm and distribute computation of the optimal policy among the agents. Distributed, optimal coordinated learning in a multi-agent variant of the multi-armed bandit problem is obtained as a special case. Consider a multi-agent system in a dynamic and uncertain environment. Each agent's local decision problem is modeled as a Markov decision process (MDP) and agents must coordinate on a joint action in each period, which provides a reward to each agent and causes local state transitions. A social planner knows the model of every agent's MDP and wants to implement the optimal joint policy, but agents are self-interested and have private local state. We provide an incentive-compatible mechanism for eliciting state information that achieves the optimal joint plan in a Markov perfect equilibrium of the induced stochastic game. In the special case in which local problems are Markov chains and agents compete to take a single action in each period, we leverage Gittins allocation indices to provide an efficient factored algorithm and distribute computation of the optimal policy among the agents. Distributed, optimal coordinated learning in a multi-agent variant of the multi-armed bandit problem is obtained as a special case. Building a dialogue agent to fulfill complex tasks, such as travel planning, is challenging because the agent has to learn to collectively complete multiple subtasks. For example, the agent needs to reserve a hotel and book a flight so that there leaves enough time for commute between arrival and hotel check-in. This paper addresses this challenge by formulating the task in the mathematical framework of options over Markov Decision Processes (MDPs), and proposing a hierarchical deep reinforcement learning approach to learning a dialogue manager that operates at different temporal scales. The dialogue manager consists of: (1) a top-level dialogue policy that selects among subtasks or options, (2) a low-level dialogue policy that selects primitive actions to complete the subtask given by the top-level policy, and (3) a global state tracker that helps ensure all cross-subtask constraints be satisfied. Experiments on a travel planning task with simulated and real users show that our approach leads to significant improvements over three baselines, two based on handcrafted rules and the other based on flat deep reinforcement learning. We consider the problem of multi-task reinforcement learning, where the agent needs to solve a sequence of Markov Decision Processes (MDPs) chosen randomly from a fixed but unknown distribution. We model the distribution over MDPs using a hierarchical Bayesian infinite mixture model. For each novel MDP, we use the previously learned distribution as an informed prior for modelbased Bayesian reinforcement learning. The hierarchical Bayesian framework provides a strong prior that allows us to rapidly infer the characteristics of new environments based on previous environments, while the use of a nonparametric model allows us to quickly adapt to environments we have not encountered before. In addition, the use of infinite mixtures allows for the model to automatically learn the number of underlying MDP components. We evaluate our approach and show that it leads to significant speedups in convergence to an optimal policy after observing only a small number of tasks. Markov Decision Processes (MDPs) provide an extensive theoretical background for problems of decision-making under uncertainty. In order to maintain computational tractability, however, real-world problems are typically discretized in states and actions as well as in time. Assuming synchronous state transitions and actions at fixed rates may result in models which are not strictly Markovian, or where agents are forced to idle between actions, losing their ability to react to sudden changes in the environment. In this work, we explore the application of Generalized Semi-Markov Decision Processes (GSMDPs) to a realistic multi-robot scenario. A case study will be presented in the domain of cooperative robotics, where real-time reactivity must be preserved, and synchronous discrete-time approaches are therefore sub-optimal. This case study is tested on a team of real robots, and also in realistic simulation. By allowing asynchronous events to be modeled over continuous time, the GSMDP approach is shown to provide greater solution quality than its discrete-time counterparts, while still being approximately solvable by existing methods. In the Markov decision process (MDP) formalization of reinforcement learning, a single adaptive agent interacts with an environment defined by a probabilistic transition function. In this solipsis-tic view, secondary agents can only be part of the environment and are therefore fixed in their behavior. The framework of Markov games allows us to widen this view to include multiple adaptive agents with interacting or competing goals. This paper considers a step in this direction in which exactly two agents with diametrically opposed goals share an environment. It describes a Q-learning-like algorithm for finding optimal policies and demonstrates its application to a simple two-player game in which the optimal policy is probabilistic. In sequential decision-making problems under uncertainty, an agent makes decisions, one after another, considering the current state of the environment where she evolves. In most work, the environment the agent evolves in is assumed to be stationary, i.e., its dynamics do not change over time. However, the stationarity hypothesis can be invalid if, for instance, exogenous events can occur. In this document, we are interested in sequential decision-making in non-stationary environments. We propose a new model named HS3MDP, allowing us to represent non-stationary problems whose dynamics evolve among a finite set of contexts. In order to efficiently solve those problems, we adapt the POMCP algorithm to HS3MDPs. We also present RLCD with SCD, a new method to learn the dynamics of the environments, without knowing a priori the number of contexts. We then explore the field of argumentation problems, where few works consider sequential decision-making. We address two types of problems: stochastic debates (APS ) and mediation problems with non-stationary agents (DMP). In this work, we present a model formalizing APS and allowing us to transform them into an MOMDP in order to optimize the sequence of arguments of one agent in the debate. We then extend this model to DMPs to allow a mediator to strategically organize speak-turns in a debate. We consider planning problems, that often arise in autonomous driving applications, in which an agent should decide on immediate actions so as to optimize a long term objective. For example, when a car tries to merge in a roundabout it should decide on an immediate acceleration braking command, while the long term effect of the command is the success failure of the merge. Such problems are characterized by continuous state and action spaces, and by interaction with multiple agents, whose behavior can be adversarial. We argue that dual versions of the MDP framework (that depend on the value function and the @math function) are problematic for autonomous driving applications due to the non Markovian of the natural state space representation, and due to the continuous state and action spaces. We propose to tackle the planning task by decomposing the problem into two phases: First, we apply supervised learning for predicting the near future based on the present. We require that the predictor will be differentiable with respect to the representation of the present. Second, we model a full trajectory of the agent using a recurrent neural network, where unexplained factors are modeled as (additive) input nodes. This allows us to solve the long-term planning problem using supervised learning techniques and direct optimization over the recurrent neural network. Our approach enables us to learn robust policies by incorporating adversarial elements to the environment. Despite the recent advances of deep reinforcement learning (DRL), agents trained by DRL tend to be brittle and sensitive to the training environment, especially in the multi-agent scenarios. In the multi-agent setting, a DRL agent’s policy can easily get stuck in a poor local optima w.r.t. its training partners – the learned policy may be only locally optimal to other agents’ current policies. In this paper, we focus on the problem of training robust DRL agents with continuous actions in the multi-agent learning setting so that the trained agents can still generalize when its opponents’ policies alter. To tackle this problem, we proposed a new algorithm, MiniMax Multi-agent Deep Deterministic Policy Gradient (M3DDPG) with the following contributions: (1) we introduce a minimax extension of the popular multi-agent deep deterministic policy gradient algorithm (MADDPG), for robust policy learning; (2) since the continuous action space leads to computational intractability in our minimax learning objective, we propose Multi-Agent Adversarial Learning (MAAL) to efficiently solve our proposed formulation. We empirically evaluate our M3DDPG algorithm in four mixed cooperative and competitive multi-agent environments and the agents trained by our method significantly outperforms existing baselines. This article addresses reinforcement learning problems based on factored Markov decision processes MDPs in which the agent must choose among a set of candidate abstractions, each build up from a different combination of state components. We present and evaluate a new approach that can perform effective abstraction selection that is more resource-efficient and or more general than existing approaches. The core of the approach is to make selection of an abstraction part of the learning agent's decision-making process by augmenting the agent's action space with internal actions that select the abstraction it uses. We prove that under certain conditions this approach results in a derived MDP whose solution yields both the optimal abstraction for the original MDP and the optimal policy under that abstraction. We examine our approach in three domains of increasing complexity: contextual bandit problems, episodic MDPs, and general MDPs with context-specific structure. © 2013 Wiley Periodicals, Inc. We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more modest goal of optimizing over some small family of policies. Specifically, we show that the family of policies associated with a low-dimensional approximation of occupancy measures yields a tractable optimization. Moreover, we propose an efficient algorithm, scaling with the size of the subspace but not the state space, that is able to find a policy with low excess loss relative to the best policy in this class. To the best of our knowledge, such results did not exist in the literature previously. We bound excess loss in the average cost and discounted cost cases, which are treated separately. Preliminary experiments show the effectiveness of the proposed algorithms in a queueing application. In this paper, we address the problem of suboptimal behavior during online partially observable Markov decision process (POMDP) planning caused by time constraints on planning. Taking inspiration from the related field of reinforcement learning (RL), our solution is to shape the agent's reward function in order to lead the agent to large future rewards without having to spend as much time explicitly estimating cumulative future rewards, enabling the agent to save time to improve the breadth planning and build higher quality plans. Specifically, we extend potential-based reward shaping (PBRS) from RL to online POMDP planning. In our extension, information about belief states is added to the function optimized by the agent during planning. This information provides hints of where the agent might find high future rewards beyond its planning horizon, and thus achieve greater cumulative rewards. We develop novel potential functions measuring information useful to agent metareasoning in POMDPs (reflecting on agent knowledge and or histories of experience with the environment), theoretically prove several important properties and benefits of using PBRS for online POMDP planning, and empirically demonstrate these results in a range of classic benchmark POMDP planning problems. In control systems theory, the Markov decision process (MDP) is a widely used optimization model involving selection of the optimal action in each state visited by a discrete-event system driven by Markov chains. The classical MDP model is suitable for an agent decision-maker interested in maximizing expected revenues, but does not account for minimizing variability in the revenues. An MDP model in which the agent can maximize the revenues while simultaneously controlling the variance in the revenues is proposed. This work is rooted in machine learning neural network concepts, where updating is based on system feedback and step sizes. First, a Bellman equation for the problem is proposed. Thereafter, convergent dynamic programming and reinforcement learning techniques for solving the MDP are provided along with encouraging numerical results on a small MDP and a preventive maintenance problem. We present two novel methods to automatically learn spatio-temporal dependencies of moving agents in complex dynamic scenes. They allow to discover temporal rules, such as the right of way between different lanes or typical traffic light sequences. To extract them, sequences of activities need to be learned. While the first method extracts rules based on a learned topic model, the second model called DDP-HMM jointly learns co-occurring activities and their time dependencies. To this end we employ Dependent Dirichlet Processes to learn an arbitrary number of infinite Hidden Markov Models. In contrast to previous work, we build on state-of-the-art topic models that allow to automatically infer all parameters such as the optimal number of HMMs necessary to explain the rules governing a scene. The models are trained offline by Gibbs Sampling using unlabeled training data.