We present the first model-free Reinforcement Learning (RL) algorithm to synthesise policies for an unknown Markov Decision Process (MDP), such that a linear time property is satisfied. The given temporal property is converted into a Limit Deterministic Buchi Automaton (LDBA) and a robust reward function is defined over the state-action pairs of the MDP according to the resulting LDBA. With this reward function, the policy synthesis procedure is "constrained" by the given specification. These constraints guide the MDP exploration so as to minimize the solution time by only considering the portion of the MDP that is relevant to satisfaction of the LTL property. This improves performance and scalability of the proposed method by avoiding an exhaustive update over the whole state space while the efficiency of standard methods such as dynamic programming is hindered by excessive memory requirements, caused by the need to store a full-model in memory. Additionally, we show that the RL procedure sets up a local value iteration method to efficiently calculate the maximum probability of satisfying the given property, at any given state of the MDP. We prove that our algorithm is guaranteed to find a policy whose traces probabilistically satisfy the LTL property if such a policy exists, and additionally we show that our method produces reasonable control policies even when the LTL property cannot be satisfied. The performance of the algorithm is evaluated via a set of numerical examples. We observe an improvement of one order of magnitude in the number of iterations required for the synthesis compared to existing approaches.
LCRL is a software tool that implements model-free Reinforcement Learning (RL) algorithms over unknown Markov Decision Processes (MDPs), synthesising policies that satisfy a given linear temporal specification with maximal probability. LCRL leverages partially deterministic finite-state machines known as Limit Deterministic Buchi Automata (LDBA) to express a given linear temporal specification. A reward function for the RL algorithm is shaped on-the-fly, based on the structure of the LDBA. Theoretical guarantees under proper assumptions ensure the convergence of the RL algorithm to an optimal …
We propose a method for efficient training of Q-functions for continuous-state Markov Decision Processes (MDPs) such that the traces of the resulting policies satisfy a given Linear Temporal Logic (LTL) property. LTL, a modal logic, can express a wide range of time-dependent logical properties (including "safety") that are quite similar to patterns in natural language. We convert the LTL property into a limit deterministic Buchi automaton and construct an on-the-fly synchronised product MDP. The control policy is then synthesised by defining an adaptive reward function and by applying a modifi…
Eindhoven University of Technology（埃因霍温理工大学）；Jheronimus Academy of Data Science（赫罗尼姆斯数据科学学院）；University of Jyväskylä（于韦斯屈莱大学）；Tilburg University（蒂尔堡大学）
We study a posterior sampling approach to efficient exploration in constrained reinforcement learning. Alternatively to existing algorithms, we propose two simple algorithms that are more efficient statistically, simpler to implement and computationally cheaper. The first algorithm is based on a linear formulation of CMDP, and the second algorithm leverages the saddle-point formulation of CMDP. Our empirical results demonstrate that, despite its simplicity, posterior sampling achieves state-of-the-art performance and, in some cases, significantly outperforms optimistic algorithms.
University at Buffalo（纽约州立大学布法罗分校）；University of Connecticut（康涅狄格大学）
Constrained reinforcement learning is to maximize the expected reward subject to constraints on utilities/costs. However, the training environment may not be the same as the test one, due to, e.g., modeling error, adversarial attack, non-stationarity, resulting in severe performance degradation and more importantly constraint violation. We propose a framework of robust constrained reinforcement learning under model uncertainty, where the MDP is not fixed but lies in some uncertainty set, the goal is to guarantee that constraints on utilities/costs are satisfied for all MDPs in the uncertainty …
Constrained reinforcement learning (RL) is an area of RL whose objective is to find an optimal policy that maximizes expected cumulative return while satisfying a given constraint. Most of the previous constrained RL works consider expected cumulative sum cost as the constraint. However, optimization with this constraint cannot guarantee a target probability of outage event that the cumulative sum cost exceeds a given threshold. This paper proposes a framework, named Quantile Constrained RL (QCRL), to constrain the quantile of the distribution of the cumulative sum cost that is a necessary and…
In this work we investigate on the concept of "restraining bolt", envisioned in Science Fiction. Specifically we introduce a novel problem in AI. We have two distinct sets of features extracted from the world, one by the agent and one by the authority imposing restraining specifications (the "restraining bolt"). The two sets are apparently unrelated since of interest to independent parties, however they both account for (aspects of) the same world. We consider the case in which the agent is a reinforcement learning agent on the first set of features, while the restraining bolt is specified log…
Inverse Reinforcement Learning (IRL) is a powerful way of learning from demonstrations. In this paper, we address IRL problems with the availability of prior knowledge that optimal policies will never violate certain constraints. Conventional approaches ignoring these constraints need many demonstrations to converge. We propose XOR-Maximum Entropy Constrained Inverse Reinforcement Learning (X-MEN), which is guaranteed to converge to the optimal policy in linear rate w.r.t. the number of learning iterations. X-MEN embeds XOR-sampling -- a provable sampling approach that transforms the #P comple…
In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maxim…
University of the Basque Country（巴斯克大学）；Lehigh University（理海大学）
This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in its formulation. Notably, we propose defining constrained combinatorial problems as fully observable Constrained Markov Decision Processes (CMDP). In that context, the solution is iteratively constructed based on interactions with the environment. The model, in addition to the reward signal, relies on penalty signals generated from constraint dissatisfactio…
In constrained reinforcement learning (RL), a learning agent seeks to not only optimize the overall reward but also satisfy the additional safety, diversity, or budget constraints. Consequently, existing constrained RL solutions require several new algorithmic ingredients that are notably different from standard RL. On the other hand, reward-free RL is independently developed in the unconstrained literature, which learns the transition dynamics without using the reward information, and thus naturally capable of addressing RL with multiple objectives under the common dynamics. This paper bridge…
We propose a successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general constrained reinforcement learning problem, which is formulated as a constrained Markov decision process (CMDP) in the context of average cost. The SCAOPO is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective and constraint functions in the original problems with convex surrogate functions. At each iteration, the convex surrogate problem can be efficiently solved by Lagrange dual method even the policy is parameter…
Institut d’intelligence aritficielle du Québec (Mila)（魁北克人工智能研究所（Mila））；École Polytechnique de Montréal（蒙特利尔理工学院）；Ubisoft La Forge（育碧La Forge实验室）；Université de Montréal（蒙特利尔大学）；ServiceNow（ServiceNow公司）
The standard formulation of Reinforcement Learning lacks a practical way of specifying what are admissible and forbidden behaviors. Most often, practitioners go about the task of behavior specification by manually engineering the reward function, a counter-intuitive process that requires several iterations and is prone to reward hacking by the agent. In this work, we argue that constrained RL, which has almost exclusively been used for safe RL, also has the potential to significantly reduce the amount of work spent for reward specification in applied RL projects. To this end, we propose to spe…
National Yang Ming Chiao Tung University（国立阳明交通大学）；Facebook AI（脸书人工智能）；Academia Sinica（中央研究院）
Action-constrained reinforcement learning (RL) is a widely-used approach in various real-world applications, such as scheduling in networked systems with resource constraints and control of a robot with kinematic constraints. While the existing projection-based approaches ensure zero constraint violation, they could suffer from the zero-gradient problem due to the tight coupling of the policy gradient and the projection, which results in sample-inefficient training and slow convergence. To tackle this issue, we propose a learning algorithm that decouples the action constraints from the policy …
Department of Electrical & Computer Engineering University of Washington（华盛顿大学电气与计算机工程系）
Constrained Markov Decision Processes are a class of stochastic decision problems in which the decision maker must select a policy that satisfies auxiliary cost constraints. This paper extends upper confidence reinforcement learning for settings in which the reward function and the constraints, described by cost functions, are unknown a priori but the transition kernel is known. Such a setting is well-motivated by a number of applications including exploration of unknown, potentially unsafe, environments. We present an algorithm C-UCRL and show that it achieves sub-linear regret ($ O(T^{\frac{…
This paper presents a constrained policy gradient algorithm. We introduce constraints for safe learning with the following steps. First, learning is slowed down (lazy learning) so that the episodic policy change can be computed with the help of the policy gradient theorem and the neural tangent kernel. Then, this enables us the evaluation of the policy at arbitrary states too. In the same spirit, learning can be guided, ensuring safety via augmenting episode batches with states where the desired action probabilities are prescribed. Finally, exogenous discounted sum of future rewards (returns) …
Clemson University（克莱姆森大学）；Université de Montréal（蒙特利尔大学）；Accenture (United States)（埃森哲（美国））；Arizona State University（亚利桑那州立大学）；Northeastern University（东北大学）
Opportunistic spectrum access is one of the emerging techniques for maximizing throughput in congested bands and is enabled by predicting idle slots in spectrum. We propose a kernel-based reinforcement learning approach coupled with a novel budget-constrained sparsification technique that efficiently captures the environment to find the best channel access actions. This approach allows learning and planning over the intrinsic state-action space and extends well to large state spaces. We apply our methods to evaluate coexistence of a reinforcement learning-based radio with a multi-channel adver…
School of Vehicle and Mobility, Tsinghua University（清华大学车辆与学院）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）
Model information can be used to predict future trajectories, so it has huge potential to avoid dangerous region when implementing reinforcement learning (RL) on real-world tasks, like autonomous driving. However, existing studies mostly use model-free constrained RL, which causes inevitable constraint violations. This paper proposes a model-based feasibility enhancement technique of constrained RL, which enhances the feasibility of policy using generalized control barrier function (GCBF) defined on the distance to constraint boundary. By using the model information, the policy can be optimize…
During initial iterations of training in most Reinforcement Learning (RL) algorithms, agents perform a significant number of random exploratory steps. In the real world, this can limit the practicality of these algorithms as it can lead to potentially dangerous behavior. Hence safe exploration is a critical issue in applying RL algorithms in the real world. This problem has been recently well studied under the Constrained Markov Decision Process (CMDP) Framework, where in addition to single-stage rewards, an agent receives single-stage costs or penalties as well depending on the state transiti…
Imperial College London（帝国理工学院）；Shanghai Jiao Tong University（上海交通大学）
Learning from Demonstration is increasingly used for transferring operator manipulation skills to robots. In practice, it is important to cater for limited data and imperfect human demonstrations, as well as underlying safety constraints. This paper presents a constrained-space optimization and reinforcement learning scheme for managing complex tasks. Through interactions within the constrained space, the reinforcement learning agent is trained to optimize the manipulation skills according to a defined reward function. After learning, the optimal policy is derived from the well-trained reinfor…
This paper describes an approach for attractor selection (or multi-stability control) in nonlinear dynamical systems with constrained actuation. Attractor selection is obtained using two different deep reinforcement learning methods: 1) the cross-entropy method (CEM) and 2) the deep deterministic policy gradient (DDPG) method. The framework and algorithms for applying these control methods are presented. Experiments were performed on a Duffing oscillator, as it is a classic nonlinear dynamical system with multiple attractors. Both methods achieve attractor selection under various control const…
The safety constraints commonly used by existing safe reinforcement learning (RL) methods are defined only on expectation of initial states, but allow each certain state to be unsafe, which is unsatisfying for real-world safety-critical tasks. In this paper, we introduce the feasible actor-critic (FAC) algorithm, which is the first model-free constrained RL method that considers statewise safety, e.g, safety for each initial state. We claim that some states are inherently unsafe no matter what policy we choose, while for other states there exist policies ensuring safety, where we say such stat…
University of California, Davis（加州大学戴维斯分校）；Shanghai Jiao Tong University（上海交通大学）；University of Minnesota（明尼苏达大学）
As mobile networks proliferate, we are experiencing a strong diversification of services, which requires greater flexibility from the existing network. Network slicing is proposed as a promising solution for resource utilization in 5G and future networks to address this dire need. In network slicing, dynamic resource orchestration and network slice management are crucial for maximizing resource utilization. Unfortunately, this process is too complex for traditional approaches to be effective due to a lack of accurate models and dynamic hidden structures. We formulate the problem as a Constrain…
This work studies reinforcement learning (RL) in the context of multi-period supply chains subject to constraints, e.g., on production and inventory. We introduce Distributional Constrained Policy Optimization (DCPO), a novel approach for reliable constraint satisfaction in RL. Our approach is based on Constrained Policy Optimization (CPO), which is subject to approximation errors that in practice lead it to converge to infeasible policies. We address this issue by incorporating aspects of distributional RL into DCPO. Specifically, we represent the return and cost value functions using neural …
In constrained reinforcement learning (C-RL), an agent seeks to learn from the environment a policy that maximizes the expected cumulative reward while satisfying minimum requirements in secondary cumulative reward constraints. Several algorithms rooted in sampled-based primal-dual methods have been recently proposed to solve this problem in policy space. However, such methods are based on stochastic gradient descent ascent algorithms whose trajectories are connected to the optimal policy only after a mixing output stage that depends on the algorithm's history. As a result, there is a mismatch…
