Uncertainty quantification remains a difficult challenge in reinforcement learning. Several algorithms exist that successfully quantify uncertainty in a practical setting. However it is unclear whether these algorithms are theoretically sound and can be expected to converge. Furthermore, they seem to treat the uncertainty in the target parameters in different ways. In this work, we unify several practical algorithms into one theoretical framework by defining a new Bellman operator on distributions, and show that this Bellman operator is a contraction. We highlight use cases of our framework by analyzing an existing Bayesian Q-learning algorithm, and also introduce a novel uncertainty-aware variant of PPO that adaptively sets its clipping hyperparameter.

The AlphaZero/MuZero (A/MZ) family of algorithms has achieved remarkable success across various challenging domains by integrating Monte Carlo Tree Search (MCTS) with learned models. Learned models introduce epistemic uncertainty, which is caused by learning from limited data and is useful for exploration in sparse reward environments. MCTS does not account for the propagation of this uncertainty however. To address this, we introduce Epistemic MCTS (EMCTS): a theoretically motivated approach to account for the epistemic uncertainty in search and harness the search for deep exploration. In the challenging sparse-reward task of writing code in the Assembly language subleq, AZ paired with our method achieves significantly higher sample efficiency over baseline AZ. Search with EMCTS solves variations of the commonly used hard-exploration benchmark Deep Sea - which baseline A/MZ are practically unable to solve - much faster than an otherwise equivalent method that does not use search for uncertainty estimation, demonstrating significant benefits from search for epistemic uncertainty estimation.

Exploration in reinforcement learning remains a difficult challenge. In order to drive exploration, ensembles with randomized prior functions have recently been popularized to quantify uncertainty in the value model. There is no theoretical reason for these ensembles to resemble the actual posterior, however. In this work, we view training ensembles from the perspective of Sequential Monte Carlo, a Monte Carlo method that approximates a sequence of distributions with a set of particles. In particular, we propose an algorithm that exploits both the practical flexibility of ensembles and theory of the Bayesian paradigm. We incorporate this method into a standard Deep Q-learning agent (DQN) and experimentally show qualitatively good uncertainty quantification and improved exploration capabilities over a regular ensemble.

Many modern reinforcement learning algorithms build on the actor-critic (AC) framework: iterative improvement of a policy (the actor) using policy improvement operators and iterative approximation of the policy's value (the critic). In contrast, the popular value-based algorithm family employs improvement operators in the value update, to iteratively improve the value function directly. In this work, we propose a general extension to the AC framework that employs two separate improvement operators: one applied to the policy in the spirit of policy-based algorithms and one applied to the value in the spirit of value-based algorithms, which we dub Value-Improved AC (VI-AC). We design two practical VI-AC algorithms based in the popular online off-policy AC algorithms TD3 and DDPG. We evaluate VI-TD3 and VI-DDPG in the Mujoco benchmark and find that both improve upon or match the performance of their respective baselines in all environments tested

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 contrast to classical reinforcement learning, distributional RL algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average
-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

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 behaviour 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 of 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.

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.

One of the most well-studied and highly performing planning approaches used in Model-Based Reinforcement Learning (MBRL) is Monte-Carlo Tree Search (MCTS). Key challenges of MCTS-based MBRL methods remain dedicated deep exploration and reliability in the face of the unknown, and both challenges can be alleviated through principled epistemic uncertainty estimation in the predictions of MCTS. We present two main contributions: First, we develop methodology to propagate epistemic uncertainty in MCTS, enabling agents to estimate the epistemic uncertainty in their predictions. Second, we utilize the propagated uncertainty for a novel deep exploration algorithm by explicitly planning to explore. We incorporate our approach into variations of MCTS-based MBRL approaches with learned and provided dynamics models, and empirically show deep exploration through successful epistemic uncertainty estimation achieved by our approach. We compare to a non-planning-based deep-exploration baseline, and demonstrate that planning with epistemic MCTS significantly outperforms non-planning based exploration in the investigated deep exploration benchmark.

In contrast to classical reinforcement learning, distributional reinforcement learning algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

Reinforcement learning agents may sometimes develop habits that are effective only when specific policies are followed. After an initial exploration phase in which agents try out different actions, they eventually converge toward a particular policy. When this occurs, the distribution of state-action trajectories becomes narrower, and agents start experiencing the same transitions again and again. At this point, spurious correlations may arise. Agents may then pick up on these correlations and learn state representations that do not generalize beyond the agent’s trajectory distribution. In this paper, we provide a mathematical characterization of this phenomenon, which we refer to as policy confounding, and show, through a series of examples, when and how it occurs in practice.

Without an assigned task, a suitable intrinsic objective for an agent is to explore the environment efficiently. However, the pursuit of exploration will inevitably bring more safety risks.
An under-explored aspect of reinforcement learning is how to achieve safe efficient exploration when the task is unknown.
In this paper, we propose a practical Constrained Entropy Maximization (CEM) algorithm to solve task-agnostic safe exploration problems, which naturally require a finite horizon and undiscounted constraints on safety costs.
The CEM algorithm aims to learn a policy that maximizes the state entropy under the premise of safety.
To avoid approximating the state density in complex domains, CEM leverages a $k$-nearest neighbor entropy estimator to evaluate the efficiency of exploration.
In terms of safety, CEM minimizes the safety costs, and adaptively trades off safety and exploration based on the current constraint satisfaction. We empirically show that CEM allows learning a safe exploration policy in complex continuous-control domains, and the learned policy benefits downstream tasks in safety and sample efficiency.

In reinforcement learning (RL), key components of many algorithms are the exploration strategy and replay buffer. These strategies regulate what environment data is collected and trained on and have been extensively studied in the RL literature. In this paper, we investigate the impact of these components in the context of generalisation in multi-task RL. We investigate the hypothesis that collecting and training on more diverse data from the training environments will improve zero-shot generalisation to new tasks. We motivate mathematically and show empirically that generalisation to tasks that are "reachable'' during training is improved by increasing the diversity of transitions in the replay buffer. Furthermore, we show empirically that this same strategy also shows improvement for generalisation to similar but "unreachable'' tasks which could be due to improved generalisation of the learned latent representations.

Safety is critical to broadening the real-world use of reinforcement learning (RL). Modeling the safety aspects using a safety-cost signal separate from the reward is becoming standard practice, since it avoids the problem of finding a good balance between safety and performance. However, the total safety-cost distribution of different trajectories is still largely unexplored. In this paper, we propose an actor critic method for safe RL that uses an implicit quantile network to approximate the distribution of accumulated safety-costs. Using an accurate estimate of the distribution of accumulated safetycosts, in particular of the upper tail of the distribution, greatly improves the performance of riskaverse RL agents. The empirical analysis shows that our method achieves good risk control in complex safety-constrained environments.

Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by exploiting a hierarchical structure with repetitive parts. This structure not only occurs naturally in robotics, but also in probabilistic programs describing, e.g., network protocols. Such programs often repeatedly call a subroutine with similar behavior. In this paper, we focus on a local case, in which the subroutines have a limited effect on the overall system state. The key ideas to accelerate analysis of such programs are (1) to treat the behavior of the subroutine as uncertain and only remove this uncertainty by a detailed analysis if needed, and (2) to abstract similar subroutines into a parametric template, and then analyse this template. These two ideas are embedded into an abstraction-refinement loop that analyses hierarchical MDPs. A prototypical implementation shows the efficacy of the approach.

The trends of autonomous transportation and mobility on demand in line with large numbers of requests increasingly call for decentralized vehicle routing optimization. Multi-agent systems (MASs) allow to model fully autonomous decentralized decision making, but are rarely considered in current decision support approaches. We propose a multi-agent approach in which autonomous vehicles are modeled as independent decision makers that locally interact with auctioneers for transportation orders. The developed MAS finds solutions for a realistic routing problem in which multiple pickup and delivery alternatives are possible per order. Although information sharing is significantly restricted, the MAS results in better solutions than a centralized Adaptive Large Neighborhood Search with full information sharing on large problem instances where computation time is limited.

Safety is critical to broadening the a lication of reinforcement learning (RL). Often, RL agents are trained in a controlled environment, such as a laboratory, before being de loyed in the real world. However, the target reward might be unknown rior to de loyment. Reward-free RL addresses this roblem by training an agent without the reward to ada t quickly once the reward is revealed. We consider the constrained reward-free setting, where an agent (the guide) learns to ex lore safely without the reward signal. This agent is trained in a controlled environment, which allows unsafe interactions and still rovides the safety signal. After the target task is revealed, safety violations are not allowed anymore. Thus, the guide is leveraged to com ose a safe sam ling olicy. Drawing from transfer learning, we also regularize a target olicy (the student) towards the guide while the student is unreliable and gradually eliminate the influence from the guide as training rogresses. The em irical analysis shows that this method can achieve safe transfer learning and hel s the student solve the target task faster.

Collaboration in transportation is important to reduce costs and emissions, but carriers may have incentives to bid strategically in decentralized auction systems. We investigate what the effect of the auction strategy is on the possible cheating benefits in a dynamic context, such that we can recommend a method with lower chances for carriers to cheat. We consider both a first-price auction system and a second-price auction scheme. Contrary to what was expected, a second-price auction scheme gives more room for successful strategic behaviour, while it also results in more rejected orders. A first-price auction scheme might be useful in practice if the profit shares that are allocated to the winner of an auction are selected carefully.

Carriers can remarkably reduce transportation costs and emissions when they collaborate, for example through a platform. Such gains, however, have only been investigated for relatively small problem instances with low numbers of carriers. We develop auction-based methods for large-scale dynamic collaborative pickup and delivery problems, combining techniques of multi-agent systems and combinatorial auctions. We evaluate our approach in terms of both solution quality and possibilities of strategic behaviour using a real-world data set of over 12,000 orders. Hence, this study is (to the best of our knowledge) the first to assess the benefits of large-scale carrier cooperation and to propose an approach for it. First, we use iterative single-order auctions to investigate possible collaboration gains for increasing numbers of carriers. Our results show that travel costs can be reduced by up to 77% when 1000 carriers collaborate, largely increasing the gains that were previously observed in smaller-scale collaboration. We also ensure that individual rationality is guaranteed in each auction. Next, we compare this approach of multiple local auctions with an established central combinatorial auction mechanism and observe that the proposed approach performs better on large-scale instances. Furthermore, to improve solution quality, we integrate the two approaches by allowing small bundle auctions in the multi-agent system. We analyze the circumstances under which bundling is beneficial in a large-scale decentralized system and demonstrate that travel cost gains of up to 13% can be obtained for 1000 carriers. Finally, we investigate whether the system is vulnerable to cheating: we show that misrepresentation of true values by individual participants sometimes can benefit them at the cost of the collective. Although such strategic behaviour is not straightforward, we also discuss different means to prevent it.