Authors: Jingduo Pan, Taoran Wu, Yiling Xue, Bai Xue
Abstract
We study stochastic minimum-cost reach-avoid reinforcement learning, where an agent must satisfy a reach-avoid specification with probability at least p while minimizing expected cumulative costs in stochastic environments. Existing safe and constrained reinforcement learning methods typically fail to jointly enforce probabilistic reach-avoid constraints and optimize cost in the learning setting in stochastic environments. To address this challenge, we introduce reach-avoid probability certificates (RAPCs), which identify states from which stochastic reach-avoid constraints are satisfiable. Building on RAPCs, we develop a contraction-based Bellman formulation that serves as a principled surrogate for integrating reach-avoid considerations into reinforcement learning, enabling cost optimization under probabilistic constraints. We establish almost sure convergence of the proposed algorithms to locally optimal policies with respect to the resulting objective. Experiments in the MuJoCo simulator demonstrate improved cost performance and consistently higher reach-avoid satisfaction rates.
Safe navigation for mobile robots demands policies that remain reliable under the high-consequence perception uncertainty of cluttered environments. Yet most existing safe reinforcement learning (RL) methods assess safety through average cumulative cost. Such metrics can mask dangerous tail-risk behaviors. To address this, we propose a framework that trains risk-sensitive policies through Conditional Value-at-Risk (CVaR) constrained optimization on an off-policy TD3 backbone and evaluates their safety margins post-training through neural network reachability verification. During training, the policy is optimized under CVaR constraints on cumulative costs, promoting sensitivity to high-cost tail outcomes rather than average behavior alone. After training, we compute action reachable sets under bounded observation uncertainty using Taylor Model analysis, yielding a safety rate metric that quantifies the proportion of evaluated states at which the policy's reachable action set remains within prescribed safety margins. A key finding is that policies trained with CVaR constraints maintain larger safety margins from obstacles across evaluated states. This makes them significantly more amenable to formal reachability verification. Experiments across ten navigation scenarios and six baselines show that our method achieves a 98.3% success rate, the highest safety verification rate among all compared methods, while revealing that average cost rankings and reachability-based safety rankings can diverge. This indicates that reachability verification captures risks which are missed by empirical cost metrics alone. We further validate our approach on a physical Clearpath Jackal robot, demonstrating successful sim-to-real transfer.
Reinforcement learning (RL) for reachability specifications is fundamental in sequential decision-making, yet theoretical guarantees remain less explored. A recent work achieves asymptotic convergence to optimal policies. However, this approach provides limited insight into convergence dynamics. In this work, we present an alternative approach that provides deeper theoretical insights into convergence. Our approach builds on PAC learning with assumptions. PAC learning guarantees near-optimal policies with high confidence in finite time but requires knowing internal MDP parameters like minimum transition probability. We argue that while these parameters are unknown in RL, they can be iteratively refined and estimated with increasing accuracy. By iteratively satisfying PAC conditions, we show that exact optimality can be achieved in the limit. Empirical evaluations on standard benchmarks validate our theoretical insights into convergence dynamics.
Amogh Palasamudram, Jakub Svoboda, Suguman Bansal +1
Deep reinforcement learning (DRL) has a longstanding tradition in addressing the reach-avoid task problem, especially for controlling robotic arms. While this task serves as a baseline environment within the research community, the ability of DRL to effectively learn the each-avoid task in complex and realistic scenarios beyond simplified and restricted tabletop settings remains uncertain. In this paper, we present, for the first time, a comprehensive benchmark for the reachavoid task that accurately captures real-world complexities without simplifications. We demonstrate a diverse range of settings for robotic arm reach-avoid task, which can be used for evaluating DRL research. We achieved this by utilizing the MuJoCo MJX physics engine and parallelizing both the simulation environment and DRL algorithms using the Brax library. We achieved state-of-the-art results with success rates of 96.1% (UR5e) and 98.8% (Franka Emika Robot) for the reach task and 86.8% (UR5e) and 95.2% (Franka) for the static reachavoid task. Our results indicate that while in previous works DRL agents could solve, for example, a reach task in a simplified setting perfectly, their agents performance collapses when evaluated in realistic scenarios. Overall, this work identifies that additional research is still required to claim the successful resolution of the robotic arm reach-avoid task using DRL. The environment and benchmarking code is available as open source at the following link