In this work, we focus on safe policy improvement in multi-agent domains where current state-of-the-art methods cannot be effectively applied because of large state and action spaces. We consider recent results using Monte Carlo Tree Search for Safe Policy Improvement with Baseline Bootstrapping and propose a novel algorithm that scales this approach to multi-agent domains, exploiting the factorization of the transition model and value function. Given a centralized behavior policy and a dataset of trajectories, our algorithm generates an improved policy by selecting joint actions using a novel extension of Max-Plus (or Variable Elimination) that constrains local actions to guarantee safety criteria. An empirical evaluation on multi-agent SysAdmin and multi-UAV Delivery shows that the approach scales to very large domains where state-of-the-art methods cannot work.
In centralized multi-agent systems, often modeled as multi-agent partially observable Markov decision processes (MPOMDPs), the action and observation spaces grow exponentially with the number of agents, making the value and belief estimation of single-agent online planning ineffective. Prior work partially tackles value estimation by exploiting the inherent structure of multi-agent settings via so-called coordination graphs. Additionally, belief estimation has been improved by incorporating the likelihood of observations into the approximation. However, the challenges of value estimation and belief estimation have only been tackled individually, which prevents existing methods from scaling to many agents. Therefore, we address these challenges simultaneously. First, we introduce weighted particle filtering to a sample-based online planner for MPOMDPs. Second, we present a scalable approximation of the belief. Third, we bring an approach that exploits the typical locality of agent interactions to novel online planning algorithms for MPOMDPs operating on a so-called sparse particle filter tree. Our experimental evaluation against several state-of-the-art baselines shows that our methods (1) are competitive in settings with only a few agents and (2) improve over the baselines in the presence of many agents.
Partial observability and uncertainty are common problems in sequential decision-making that particularly impede the use of formal models such as Markov decision processes (MDPs).
However, in practice, agents may be able to employ costly sensors to measure their environment and resolve partial observability by gathering information. Moreover, imprecise transition functions can capture model uncertainty. We combine these concepts and extend MDPs to robust active-measuring MDPs (RAM-MDPs). We present an active-measure heuristic to solve RAM-MDPs efficiently and show that model uncertainty can, counterintuitively, let agents take fewer measurements. We propose a method to counteract this behavior while only incurring a bounded additional cost. We empirically compare our methods to several baselines and show their superior scalability and performance.
Large-scale infrastructure systems are crucial for societal welfare, and their effective management requires strategic forecasting and intervention methods that account for various complexities. Our study addresses two challenges within the Prognostics and Health Management (PHM) framework applied to sewer assets: modeling pipe degradation across severity levels and developing effective maintenance policies. We employ Multi-State Degradation Models (MSDM) to represent the stochastic degradation process in sewer pipes and use Deep Reinforcement Learning (DRL) to devise maintenance strategies. A case study of a Dutch sewer network exemplifies our methodology. Our findings demonstrate the model’s effectiveness in generating intelligent, cost-saving maintenance strategies that surpass heuristics. It adapts its management strategy based on the pipe’s age, opting for a passive approach for newer pipes and transitioning to active strategies for older ones to prevent failures and reduce costs. This research highlights DRL’s potential in optimizing maintenance policies. Future research will aim improve the model by incorporating partial observability, exploring various reinforcement learning algorithms, and extending this methodology to comprehensive infrastructure management.
Safety is critical to broadening the application of reinforcement learning (RL). Often, we train RL agents in a controlled environment, such as a laboratory, before deploying them in the real world. However, the real-world target task might be unknown prior to deployment. Reward-free RL trains an agent without the reward to adapt quickly once the reward is revealed. We consider the constrained reward-free setting, where an agent (the guide) learns to explore safely without the reward signal. This agent is trained in a controlled environment, which allows unsafe interactions and still provides the safety signal. After the target task is revealed, safety violations are not allowed anymore. Thus, the guide is leveraged to compose a safe behavior policy. Drawing from transfer learning, we also regularize a target policy (the student) towards the guide while the student is unreliable and gradually eliminate the influence from the guide as training progresses. The empirical analysis shows that this method can achieve safe transfer learning and helps the student solve the target task faster.
Automated curriculum generation for reinforcement learning (RL) aims to speed up learning by designing a sequence of tasks of increasing difficulty. Such tasks are usually drawn from probability distributions with exponentially bounded tails, such as uniform or Gaussian distributions. However, existing approaches overlook heavy-tailed distributions. Under such distributions, current methods may fail to learn optimal policies in rare and risky tasks, which fall under the tails and yield the lowest returns, respectively. We address this challenge by proposing a risk-aware curriculum generation algorithm that simultaneously creates two curricula: 1) a primary curriculum that aims to maximize the expected discounted return with respect to a distribution over target tasks, and an auxiliary curriculum that identifies and over-samples rare and risky tasks observed in the primary curriculum. Our empirical results evidence that the proposed algorithm achieves significantly higher returns in frequent as well as rare tasks compared to the state-of-the-art methods.
Algorithms for safely improving policies are important to deploy reinforcement learning approaches in real-world scenarios. In this work, we propose an algorithm, called MCTS-SPIBB, that computes safe policy improvement online using a Monte Carlo Tree Search based strategy. We theoretically prove that the policy generated by MCTS-SPIBB converges, as the number of simulations grows, to the optimal safely improved policy generated by Safe Policy Improvement with Baseline Bootstrapping (SPIBB), a popular algorithm based on policy iteration. Moreover, our empirical analysis performed on three standard benchmark domains shows that MCTS-SPIBB scales to significantly larger problems than SPIBB because it computes the policy online and locally, i.e., only in the states actually visited by the agent.
In an offline reinforcement learning setting, the safe policy improvement (SPI) problem aims to improve the performance of a behavior policy according to which sample data has been generated. State-of-the-art approaches to SPI require a high number of samples to provide practical probabilistic guarantees on the improved policy’s performance. We present a novel approach to the SPI problem that provides the means to require less data for such guarantees. Specifically, to prove the correctness of these guarantees, we devise implicit transformations on the data set and the underlying environment model that serve as theoretical foundations to derive tighter improvement bounds for SPI. Our empirical evaluation, using the well-established SPI with baseline bootstrapping (SPIBB) algorithm, on standard benchmarks shows that our method indeed significantly reduces the sample complexity of the SPIBB algorithm.
We present recursive small-step multi-agent A* (RS-MAA*), an exact algorithm that optimizes the expected reward in decentralized partially observable Markov decision processes (Dec-POMDPs). RS-MAA* builds on multi-agent A* (MAA*), an algorithm that finds policies by exploring a search tree, but tackles two major scalability concerns. First, we employ a modified, small-step variant of the search tree that avoids the double exponential outdegree of the classical formulation. Second, we use a tight and recursive heuristic that we compute on-the-fly, thereby avoiding an expensive precomputation. The resulting algorithm is conceptually simple, yet it shows superior performance on a rich set of standard benchmarks.
ICAPS
Act-Then-Measure: Reinforcement Learning for Partially Observable Environments with Active Measuring
We study Markov decision processes (MDPs) where agents have direct control over when and how they gather information, as formalized by action-contingent noiselessly observable MDPs (ACNO-MPDs). In these models, actions consist of two components: a control action which affects the environment, and a measurement action which affects what the agent can observe. For solving ACNO-MDPs, we introduce the act-then-measure (ATM) heuristic, which assumes that we can ignore future state uncertainty when choosing control actions. We show how following this heuristic may lead to shorter policy computation times and prove a bound on the performance loss incurred by the heuristic. To decide whether or not to take a measurement action, we introduce the concept of measuring value. We develop a reinforcement learning algorithm based on the ATM heuristic, using a variant of Dyna-Q modified for partially observable domains, and showcase its superior performance in comparison to prior methods on a number of partially-observable environments.
We address the problem of safe reinforcement learning from pixel observations. Inherent challenges in such settings are (1) a trade-off between reward optimization and adhering to safety constraints, (2) partial observability, and (3) high-dimensional observations. We formalize the problem in a constrained, partially observable Markov decision process framework, where an agent obtains distinct reward and safety signals. To address the curse of dimensionality, we employ a novel safety critic using the stochastic latent actor-critic (SLAC) approach. The latent variable model predicts rewards and safety violations, and we use the safety critic to train safe policies. Using well-known benchmark environments, we demonstrate competitive performance over existing approaches regarding computational requirements, final reward return, and satisfying the safety constraints.
We study safe policy improvement (SPI) for partially observable Markov decision processes (POMDPs). SPI is an offline reinforcement learning (RL) problem that assumes access to (1) historical data about an environment, and (2) the so-called behavior policy that previously generated this data by interacting with the environment. SPI methods neither require access to a model nor the environment itself, and aim to reliably improve the behavior policy in an offline manner. Existing methods make the strong assumption that the environment is fully observable. In our novel approach to the SPI problem for POMDPs, we assume that a finite-state controller (FSC) represents the behavior policy and that finite memory is sufficient to derive optimal policies. This assumption allows us to map the POMDP to a finite-state fully observable MDP, the history MDP. We estimate this MDP by combining the historical data and the memory of the FSC, and compute an improved policy using an off-the-shelf SPI algorithm. The underlying SPI method constrains the policy-space according to the available data, such that the newly computed policy only differs from the behavior policy when sufficient data was available. We show that this new policy, converted into a new FSC for the (unknown) POMDP, outperforms the behavior policy with high probability. Experimental results on several well-established benchmarks show the applicability of the approach, even in cases where finite memory is not sufficient.
Deep Reinforcement Learning (RL) agents are susceptible to adversarial noise in their observations that can mislead their policies and decrease their performance. However, an adversary may be interested not only in decreasing the reward, but also in modifying specific temporal logic properties of the policy. This paper presents a metric that measures the exact impact of adversarial attacks against such properties. We use this metric to craft optimal adversarial attacks. Furthermore, we introduce a model checking method that allows us to verify the robustness of RL policies against adversarial attacks. Our empirical analysis confirms (1) the quality of our metric to craft adversarial attacks against temporal logic properties, and (2) that we are able to concisely assess a system’s robustness against attacks.
STTT
Decision-making under uncertainty: beyond probabilities. Challenges and Perspectives
This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty that goes beyond this classical interpretation, particularly by employing a clear distinction between aleatoric and epistemic uncertainty. The paper features an overview of Markov decision processes (MDPs) and extensions to account for partial observability and adversarial behavior. These models sufficiently capture aleatoric uncertainty but fail to account for epistemic uncertainty robustly. Consequently, we present a thorough overview of so-called uncertainty models that exhibit uncertainty in a more robust interpretation. We show several solution techniques for both discrete and continuous models, ranging from formal verification, over control-based abstractions, to reinforcement learning. As an integral part of this paper, we list and discuss several key challenges that arise when dealing with rich types of uncertainty in a model-based fashion.
Markov decision processes (MDPs) are formal models commonly used in sequential decision-making. MDPs capture the stochasticity that may arise, for instance, from imprecise actuators via probabilities in the transition function. However, in data-driven applications, deriving precise probabilities from (limited) data introduces statistical errors that may lead to unexpected or undesirable outcomes. Uncertain MDPs (uMDPs) do not require precise probabilities but instead use so-called uncertainty sets in the transitions, accounting for such limited data. Tools from the formal verification community efficiently compute robust policies that provably adhere to formal specifications, like safety constraints, under the worst-case instance in the uncertainty set. We continuously learn the transition probabilities of an MDP in a robust anytime-learning approach that combines a dedicated Bayesian inference scheme with the computation of robust policies. In particular, our method (1) approximates probabilities as intervals, (2) adapts to new data that may be inconsistent with an intermediate model, and (3) may be stopped at any time to compute a robust policy on the uMDP that faithfully captures the data so far. We show the effectiveness of our approach and compare it to robust policies computed on uMDPs learned by the UCRL2 reinforcement learning algorithm in an experimental evaluation on several benchmarks.
Safety is critical to broadening the real-world use of reinforcement learning. Modeling the safety aspects using a safety-cost signal separate from the reward and bounding the expected safety-cost is becoming standard practice, since it avoids the problem of finding a good balance between safety and performance. However, it can be risky to set constraints only on the expectation neglecting the tail of the distribution, which might have prohibitively large values. In this paper, we propose a method called Worst-Case Soft Actor Critic for safe RL that approximates the distribution of accumulated safety-costs to achieve risk control. More specifically, a certain level of conditional Value-at-Risk from the distribution is regarded as a safety constraint, which guides the change of adaptive safety weights to achieve a trade-off between reward and safety. As a result, we can compute policies whose worst-case performance satisfies the constraints. We investigate two ways to estimate the safety-cost distribution, namely a Gaussian approximation and a quantile regression algorithm. On the one hand, the Gaussian approximation is simple and easy to implement, but may underestimate the safety cost, on the other hand, the quantile regression leads to a more conservative behavior. The empirical analysis shows that the quantile regression method achieves excellent results in complex safety-constrained environments, showing good risk control.
The use of reinforcement learning (RL) in real-world domains often requires extensive effort to ensure safe behavior. While this compromises the autonomy of the system, it might still be too risky to allow a learning agent to freely explore its environment. These strict impositions come at the cost of flexibility and applying them often relies on complex parameters and hard-coded knowledge modelled by the reward function. Autonomous driving is one such domain that could greatly benefit from more efficient and verifiable methods for safe automation. We propose to approach the automated driving problem using constrained RL, a method that automates the trade off between risk and utility, thereby significantly reducing the burden on the designer. We first show that an engineered reward function for ensuring safety and utility in one specific environment might not result in the optimal behavior when traffic dynamics changes in the exact environment. Next we show how algorithms based on constrained RL which are more robust to the environmental disturbances can address this challenge. These algorithms use a simple and easy to interpret reward and cost function, and are able to maintain both, efficiency and safety without requiring reward parameter tuning. We demonstrate our approach in the automated merging scenario with different traffic configurations such as low or high chance of cooperative drivers and different cooperative driving strategies.
Deploying reinforcement learning (RL) involves major concerns around safety. Engineering a reward signal that allows the agent to maximize its performance while remaining safe is not trivial. Safe RL studies how to mitigate such problems. For instance, we can decouple safety from reward using constrained Markov decision processes (CMDPs), where an independent signal models the safety aspects. In this setting, an RL agent can autonomously find tradeoffs between performance and safety. Unfortunately, most RL agents designed for CMDPs only guarantee safety after the learning phase, which might prevent their direct deployment. In this work, we investigate settings where a concise abstract model of the safety aspects is given, a reasonable assumption since a thorough understanding of safety-related matters is a prerequisite for deploying RL in typical applications. Factored CMDPs provide such compact models when a small subset of features describe the dynamics relevant for the safety constraints. We propose an RL algorithm that uses this abstract model to learn policies for CMDPs safely, that is without violating the constraints. During the training process, this algorithm can seamlessly switch from a conservative policy to a greedy policy without violating the safety constraints. We prove that this algorithm is safe under the given assumptions. Empirically, we show that even if safety and reward signals are contradictory, this algorithm always operates safely and, when they are aligned, this approach also improves the agent’s performance.
Safe exploration is regarded as a key priority area for reinforcement learning research. With separate reward and safety signals, it is natural to cast it as constrained reinforcement learning, where expected long-term costs of policies are constrained. However, it can be hazardous to set constraints on the expected safety signal without considering the tail of the distribution. For instance, in safety-critical domains, worst-case analysis is required to avoid disastrous results. We present a novel reinforcement learning algorithm called Worst-Case Soft Actor Critic, which extends the Soft Actor Critic algorithm with a safety critic to achieve risk control. More specifically, a certain level of conditional Value-at-Risk from the distribution is regarded as a safety measure to judge the constraint satisfaction, which guides the change of adaptive safety weights to achieve a trade-off between reward and safety. As a result, we can optimize policies under the premise that their worst-case performance satisfies the constraints. The empirical analysis shows that our algorithm attains better risk control compared to expectation-based methods.
Previous work has shown the unreliability of existing algorithms in the batch Reinforcement Learning setting, and proposed the theoretically-grounded Safe Policy Improvement with Baseline Bootstrapping (SPIBB) fix: reproduce the baseline policy in the uncertain state-action pairs, in order to control the variance on the trained policy performance. However, in many real-world applications such as dialogue systems, pharmaceutical tests or crop management, data is collected under human supervision and the baseline remains unknown. In this paper, we apply SPIBB algorithms with a baseline estimate built from the data. We formally show safe policy improvement guarantees over the true baseline even without direct access to it. Our empirical experiments on finite and continuous states tasks support the theoretical findings. It shows little loss of performance in comparison with SPIBB when the baseline policy is given, and more importantly, drastically and significantly outperforms competing algorithms both in safe policy improvement, and in average performance.
Reinforcement Learning (RL) deals with problems that can be modeled as a Markov Decision Process (MDP) where the transition function is unknown. In situations where an arbitrary policy pi is already in execution and the experiences with the environment were recorded in a batch D, an RL algorithm can use D to compute a new policy pi’. However, the policy computed by traditional RL algorithms might have worse performance compared to pi. Our goal is to develop safe RL algorithms, where the agent has a high confidence that the performance of pi’ is better than the performance of pi given D. To develop sample-efficient and safe RL algorithms we combine ideas from exploration strategies in RL with a safe policy improvement method.
We investigate how Safe Policy Improvement (SPI) algorithms can exploit the structure of factored Markov decision processes when such structure is unknown a priori. To facilitate the application of reinforcement learning in the real world, SPI provides probabilistic guarantees that policy changes in a running process will improve the performance of this process. However, current SPI algorithms have requirements that might be impractical, such as: (i) availability of a large amount of historical data, or (ii) prior knowledge of the underlying structure. To overcome these limitations we enhance a Factored SPI (FSPI) algorithm with different structure learning methods. The resulting algorithms need fewer samples to improve the policy and require weaker prior knowledge assumptions. In well-factorized domains, the proposed algorithms improve performance significantly compared to a flat SPI algorithm, demonstrating a sample complexity closer to an FSPI algorithm that knows the structure. This indicates that the combination of FSPI and structure learning algorithms is a promising solution to real-world problems involving many variables.
We present a novel safe reinforcement learning algorithm that exploits the factored dynamics of the environment to become less conservative. We focus on problem settings in which a policy is already running and the interaction with the environment is limited. In order to safely deploy an updated policy, it is necessary to provide a confidence level regarding its expected performance. However, algorithms for safe policy improvement might require a large number of past experiences to become confident enough to change the agent’s behavior. It can achieve a better sample complexity by exploiting independence between features of the environment, but it lacks a confidence level. We study how to improve the sample efficiency of the safe policy improvement with baseline bootstrapping algorithm by exploiting the factored structure of the environment. Our main result is a theoretical bound that is linear in the number of parameters of the factored representation instead of the number of states. The empirical analysis shows that our method can improve the policy using a number of samples potentially one order of magnitude smaller than the flat algorithm.
2018
ICML workshop
An Empirical Evaluation of Safe Policy Improvement in Factored Environments
Reinforcement Learning (RL) deals with problems that can be modeled as a Markov Decision Process (MDP) where the transition function is unknown. In situations where an arbitrary policy π is already in execution and the experiences with the environment were recorded in a batch D, an RL algorithm can use to compute a new policy π’. However, the policy computed by traditional RL algorithms might have worse performance compared to π. Our goal is to develop safe RL algorithms, where the agent has a high confidence that the performance of π’ is better than the performance of π given D. To develop sample-efficient and safe RL algorithms we combine ideas from exploration strategies in RL with a safe policy improvement method.
In many realistic planning situations, any policy has a non-zero probability of reaching a dead-end. In such cases, a popular approach is to plan to maximize the probability of reaching the goal. While this strategy increases the robustness and expected autonomy of the robot, it considers that the robot gives up on the task whenever a dead-end is encountered. In this work, we consider planning for agents that pro-actively and autonomously resort to human help when an unavoidable dead-end is encountered (the so-called symbiotic agents). To this end, we develop a new class of Goal-Oriented Markov Decision Process that includes a set of human actions that ensures the existence of a proper policy, one that possibly resorts to human help. We discuss two different optimization criteria: minimizing the probability to use human help and minimizing the expected cumulative cost with a finite penalty for using human help for the first time. We show that for a large enough penalty both criteria are equivalent. We report on experiments with standard probabilistic planning domains for reasonably large problems.
2016
ENIAC
Heuristics for Dead-Ends Detection in Probabilisitic Planning