Abstract The difficulty of manually specifying reward functions has led to an interest in using linear temporal logic (LTL) to express objectives for reinforcement learning (RL). However, LTL has the downside that it is sensitive to small perturbations in the transition probabilities, which prevents probably approximately correct (PAC) learning without additional assumptions. Time discounting provides a way of removing this sensitivity, while retaining the high expressivity of the logic. We study the use of discounted LTL for policy synthesis in Markov decision processes with unknown transition probabilities, and show how to reduce discounted LTL to discounted-sum reward via a reward machine when all discount factors are identical.

Compositional reinforcement learning is a promising approach for training policies to perform complex long-horizon tasks. Typically, a high-level task is decomposed into a sequence of subtasks and a separate policy is trained to perform each subtask. In this paper, we focus on the problem of training subtask policies in a way that they can be used to perform any task; here, a task is given by a sequence of subtasks. We aim to maximize the worst-case performance over all tasks as opposed to the average-case performance. We formulate the problem as a two agent zero-sum game in which the adversary picks the sequence of subtasks. We propose two RL algorithms to solve this game: one is an adaptation of existing multi-agent RL algorithms to our setting and the other is an asynchronous version which enables parallel training of subtask policies. We evaluate our approach on two multi-task environments with continuous states and actions and demonstrate that our algorithms outperform state-of-the-art baselines.

Abstract Reinforcement learning has been shown to be an effective strategy for automatically training policies for challenging control problems. Focusing on non-cooperative multi-agent systems, we propose a novel reinforcement learning framework for training joint policies that form a Nash equilibrium. In our approach, rather than providing low-level reward functions, the user provides high-level specifications that encode the objective of each agent. Then, guided by the structure of the specifications, our algorithm searches over policies to identify one that provably forms an $$\epsilon $$ ϵ -Nash equilibrium (with high probability). Importantly, it prioritizes policies in a way that maximizes social welfare across all agents. Our empirical evaluation demonstrates that our algorithm computes equilibrium policies with high social welfare, whereas state-of-the-art baselines either fail to compute Nash equilibria or compute ones with comparatively lower social welfare.

We propose a novel hierarchical reinforcement learning framework for control with continuous state and action spaces. In our framework, the user specifies subgoal regions which are subsets of states; then, we (i) learn options that serve as transitions between these subgoal regions, and (ii) construct a high-level plan in the resulting abstract decision process (ADP). A key challenge is that the ADP may not be Markov; we propose two algorithms for planning in the ADP that address this issue. Our first algorithm is conservative, allowing us to prove theoretical guarantees on its performance, which help inform the design of subgoal regions. Our second algorithm is a practical one that interweaves planning at the abstract level and learning at the concrete level. In our experiments, we demonstrate that our approach outperforms state-of-the-art hierarchical reinforcement learning algorithms on several challenging benchmarks.

We study the problem of learning control policies for complex tasks given by logical specifications. Recent approaches automatically generate a reward function from a given specification and use a suitable reinforcement learning algorithm to learn a policy that maximizes the expected reward. These approaches, however, scale poorly to complex tasks that require high-level planning. In this work, we develop a compositional learning approach, called DIRL, that interleaves high-level planning and reinforcement learning. First, DIRL encodes the specification as an abstract graph; intuitively, vertices and edges of the graph correspond to regions of the state space and simpler sub-tasks, respectively. Our approach then incorporates reinforcement learning to learn neural network policies for each edge (sub-task) within a Dijkstra-style planning algorithm to compute a high-level plan in the graph. An evaluation of the proposed approach on a set of challenging control benchmarks with continuous state and action spaces demonstrates that it outperforms state-of-the-art baselines.

Recent advances in deep learning have enabled data-driven controller design for autonomous systems. However, verifying safety of such controllers, which are often hard-to-analyze neural networks, remains a challenge. Inspired by compositional strategies for program verification, we propose a framework for compositional learning and verification of neural network controllers. Our approach is to decompose the task (e.g., car navigation) into a sequence of subtasks (e.g., segments of the track), each corresponding to a different mode of the system (e.g., go straight or turn). Then, we learn a separate controller for each mode, and verify correctness by proving that (i) each controller is correct within its mode, and (ii) transitions between modes are correct. This compositional strategy not only improves scalability of both learning and verification, but also enables our approach to verify correctness for arbitrary compositions of the subtasks. To handle partial observability (e.g., LiDAR), we additionally learn and verify a mode predictor that predicts which controller to use. Finally, our framework also incorporates an algorithm that, given a set of controllers, automatically synthesizes the pre- and postconditions required by our verification procedure. We validate our approach in a case study on a simulation model of the F1/10 autonomous car, a system that poses challenges for existing verification tools due to both its reliance on LiDAR observations, as well as the need to prove safety for complex track geometries. We leverage our framework to learn and verify a controller that safely completes any track consisting of an arbitrary sequence of five kinds of track segments.

Real-time decision making in IoT applications relies upon space-efficient evaluation of queries over streaming data. To model the uncertainty in the classification of data being processed, we consider the model of probabilistic strings --- sequences of discrete probability distributions over a finite set of events, and initiate the study of space complexity of streaming computation for different classes of queries over such probabilistic strings.

Reinforcement learning is a promising approach for learning control policies for robot tasks. However, specifying complex tasks (e.g., with multiple objectives and safety constraints) can be challenging, since the user must design a reward function that encodes the entire task. Furthermore, the user often needs to manually shape the reward to ensure convergence of the learning algorithm. We propose a language for specifying complex control tasks, along with an algorithm that compiles specifications in our language into a reward function and automatically performs reward shaping. We implement our approach in a tool called SPECTRL, and show that it outperforms several state-of-the-art baselines.