Efficient Duple Perturbation Robustness in Low-rank MDPs

The pursuit of robustness has recently been a popular topic in reinforcement learning (RL) research, yet the existing methods generally suffer from efficiency issues that obstruct their real-world implementation. In this paper, we introduce duple perturbation robustness, i.e. perturbation on both the feature and factor vectors for low-rank Markov decision processes (MDPs), via a novel characterization of $(\xi,\eta)$-ambiguity sets. The novel robust MDP formulation is compatible with the function representation view, and therefore, is naturally applicable to practical RL problems with large or even continuous state-action spaces. Meanwhile, it also gives rise to a provably efficient and practical algorithm with theoretical convergence rate guarantee. Examples are designed to justify the new robustness concept, and algorithmic efficiency is supported by both theoretical bounds and numerical simulations.

Skill Transfer and Discovery for Sim-to-Real Learning: A Representation-Based Viewpoint

We study sim-to-real skill transfer and discovery in the context of robotics control using representation learning. We draw inspiration from spectral decomposition of Markov decision processes. The spectral decomposition brings about representation that can linearly represent the state-action value function induced by any policies, thus can be regarded as skills. The skill representations are transferable across arbitrary tasks with the same transition dynamics. Moreover, to handle the sim-to-real gap in the dynamics, we propose a skill discovery algorithm that learns new skills caused by the sim-to-real gap from real-world data. We promote the discovery of new skills by enforcing orthogonal constraints between the skills to learn and the skills from simulators, and then synthesize the policy using the enlarged skill sets. We demonstrate our methodology by transferring quadrotor controllers from simulators to Crazyflie 2.1 quadrotors. We show that we can learn the skill representations from a single simulator task and transfer these to multiple different real-world tasks including hovering, taking off, landing and trajectory tracking. Our skill discovery approach helps narrow the sim-to-real gap and improve the real-world controller performance by up to 30.2%.

Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimization

We study the multi-agent Bayesian optimization (BO) problem, where multiple agents maximize a black-box function via iterative queries. We focus on Entropy Search (ES), a sample-efficient BO algorithm that selects queries to maximize the mutual information about the maximum of the black-box function. One of the main challenges of ES is that calculating the mutual information requires computationally-costly approximation techniques. For multi-agent BO problems, the computational cost of ES is exponential in the number of agents. To address this challenge, we propose the Gaussian Max-value Entropy Search, a multi-agent BO algorithm with favorable sample and computational efficiency. The key to our idea is to use a normal distribution to approximate the function maximum and calculate its mutual information accordingly. The resulting approximation allows queries to be cast as the solution of a closed-form optimization problem which, in turn, can be solved via a modified gradient ascent algorithm and scaled to a large number of agents. We demonstrate the effectiveness of Gaussian max-value Entropy Search through numerical experiments on standard test functions and real-robot experiments on the source-seeking problem. Results show that the proposed algorithm outperforms the multi-agent BO baselines in the numerical experiments and can stably seek the source with a limited number of noisy observations on real robots.

Safe Model-Based Reinforcement Learning with an Uncertainty-Aware Reachability Certificate

Safe reinforcement learning (RL) that solves constraint-satisfactory policies provides a promising way to the broader safety-critical applications of RL in real-world problems such as robotics. Among all safe RL approaches, model-based methods reduce training time violations further due to their high sample efficiency. However, lacking safety robustness against the model uncertainties remains an issue in safe model-based RL, especially in training time safety. In this paper, we propose a distributional reachability certificate (DRC) and its Bellman equation to address model uncertainties and characterize robust persistently safe states. Furthermore, we build a safe RL framework to resolve constraints required by the DRC and its corresponding shield policy. We also devise a line search method to maintain safety and reach higher returns simultaneously while leveraging the shield policy. Comprehensive experiments on classical benchmarks such as constrained tracking and navigation indicate that the proposed algorithm achieves comparable returns with much fewer constraint violations during training.

Synthesize Efficient Safety Certificates for Learning-Based Safe Control using Magnitude Regularization

Energy-function-based safety certificates can provide provable safety guarantees for the safe control tasks of complex robotic systems. However, all recent studies about learning-based energy function synthesis only consider the feasibility, which might cause over-conservativeness and result in less efficient controllers. In this work, we proposed the magnitude regularization technique to improve the efficiency of safe controllers by reducing the conservativeness inside the energy function while keeping the promising provable safety guarantees. Specifically, we quantify the conservativeness by the magnitude of the energy function, and we reduce the conservativeness by adding a magnitude regularization term to the synthesis loss. We propose the SafeMR algorithm that uses reinforcement learning (RL) for the synthesis to unify the learning processes of safe controllers and energy functions. Experimental results show that the proposed method does reduce the conservativeness of the energy functions and outperforms the baselines in terms of the controller efficiency while guaranteeing safety.

Reachability Constrained Reinforcement Learning

Constrained Reinforcement Learning (CRL) has gained significant interest recently, since the satisfaction of safety constraints is critical for real world problems. However, existing CRL methods constraining discounted cumulative costs generally lack rigorous definition and guarantee of safety. On the other hand, in the safe control research, safety is defined as persistently satisfying certain state constraints. Such persistent safety is possible only on a subset of the state space, called feasible set, where an optimal largest feasible set exists for a given environment. Recent studies incorporating safe control with CRL using energy-based methods such as control barrier function (CBF), safety index (SI) leverage prior conservative estimation of feasible sets, which harms performance of the learned policy. To deal with this problem, this paper proposes a reachability CRL (RCRL) method by using reachability analysis to characterize the largest feasible sets. We characterize the feasible set by the established self-consistency condition, then a safety value function can be learned and used as constraints in CRL. We also use the multi-time scale stochastic approximation theory to prove that the proposed algorithm converges to a local optimum, where the largest feasible set can be guaranteed. Empirical results on different benchmarks such as safe-control-gym and Safety-Gym validate the learned feasible set, the performance in optimal criteria, and constraint satisfaction of RCRL, compared to state-of-the-art CRL baselines.

Learn Zero-Constraint-Violation Policy in Model-Free Constrained Reinforcement Learning

In the trial-and-error mechanism of reinforcement learning (RL), a notorious contradiction arises when we expect to learn a safe policy: how to learn a safe policy without enough data and prior model about the dangerous region? Existing methods mostly use the posterior penalty for dangerous actions, which means that the agent is not penalized until experiencing danger. This fact causes that the agent cannot learn a zero-violation policy even after convergence. Otherwise, it would not receive any penalty and lose the knowledge about danger. In this paper, we propose the safe set actor-critic (SSAC) algorithm, which confines the policy update using safety-oriented energy functions, or the safety indexes. The safety index is designed to increase rapidly for potentially dangerous actions, which allows us to locate the safe set on the action space, or the control safe set. Therefore, we can identify the dangerous actions prior to taking them, and further obtain a zero constraint-violation policy after convergence.We claim that we can learn the energy function in a model-free manner similar to learning a value function. By using the energy function transition as the constraint objective, we formulate a constrained RL problem. We prove that our Lagrangian-based solutions make sure that the learned policy will converge to the constrained optimum under some assumptions. The proposed algorithm is evaluated on both the complex simulation environments and a hardware-in-loop (HIL) experiment with a real controller from the autonomous vehicle. Experimental results suggest that the converged policy in all environments achieves zero constraint violation and comparable performance with model-based baselines.

Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning

Safety is the major consideration in controlling complex dynamical systems using reinforcement learning (RL), where the safety certificate can provide provable safety guarantee. A valid safety certificate is an energy function indicating that safe states are with low energy, and there exists a corresponding safe control policy that allows the energy function to always dissipate. The safety certificate and the safe control policy are closely related to each other and both challenging to synthesize. Therefore, existing learning-based studies treat either of them as prior knowledge to learn the other, which limits their applicability with general unknown dynamics. This paper proposes a novel approach that simultaneously synthesizes the energy-function-based safety certificate and learns the safe control policy with CRL. We do not rely on prior knowledge about either an available model-based controller or a perfect safety certificate. In particular, we formulate a loss function to optimize the safety certificate parameters by minimizing the occurrence of energy increases. By adding this optimization procedure as an outer loop to the Lagrangian-based constrained reinforcement learning (CRL), we jointly update the policy and safety certificate parameters and prove that they will converge to their respective local optima, the optimal safe policy and a valid safety certificate. We evaluate our algorithms on multiple safety-critical benchmark environments. The results show that the proposed algorithm learns provably safe policies with no constraint violation. The validity or feasibility of synthesized safety certificate is also verified numerically.

Feasible Actor-Critic: Constrained Reinforcement Learning for Ensuring Statewise Safety

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 states and policies are feasible. By constructing a statewise Lagrange function available on RL sampling and adopting an additional neural network to approximate the statewise Lagrange multiplier, we manage to obtain the optimal feasible policy which ensures safety for each feasible state and the safest possible policy for infeasible states. Furthermore, the trained multiplier net can indicate whether a given state is feasible or not through the statewise complementary slackness condition. We provide theoretical guarantees that FAC outperforms previous expectation-based constrained RL methods in terms of both constraint satisfaction and reward optimization. Experimental results on both robot locomotive tasks and safe exploration tasks verify the safety enhancement and feasibility interpretation of the proposed method.