Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systems

Learning to move is a primary goal for animals and robots, where ensuring safety is often important when optimizing control policies on the embodied systems. For complex tasks such as the control of human or humanoid control, the high-dimensional parameter space adds complexity to the safe optimization effort. Current safe exploration algorithms exhibit inefficiency and may even become infeasible with large high-dimensional input spaces. Furthermore, existing high-dimensional constrained optimization methods neglect safety in the search process. In this paper, we propose High-dimensional Safe Bayesian Optimization with local optimistic exploration (HdSafeBO), a novel approach designed to handle high-dimensional sampling problems under probabilistic safety constraints. We introduce a local optimistic strategy to efficiently and safely optimize the objective function, providing a probabilistic safety guarantee and a cumulative safety violation bound. Through the use of isometric embedding, HdSafeBO addresses problems ranging from a few hundred to several thousand dimensions while maintaining safety guarantees. To our knowledge, HdSafeBO is the first algorithm capable of optimizing the control of high-dimensional musculoskeletal systems with high safety probability. We also demonstrate the real-world applicability of HdSafeBO through its use in the safe online optimization of neural stimulation induced human motion control.

Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes

Bayesian optimization is an effective technique for black-box optimization, but its applicability is typically limited to low-dimensional and small-budget problems due to the cubic complexity of computing the Gaussian process (GP) surrogate. While various approximate GP models have been employed to scale Bayesian optimization to larger sample sizes, most suffer from overly-smooth estimation and focus primarily on problems that allow for large online samples. In this work, we argue that Bayesian optimization algorithms with sparse GPs can more efficiently allocate their representational power to relevant regions of the search space. To achieve this, we propose focalized GP, which leverages a novel variational loss function to achieve stronger local prediction, as well as FocalBO, which hierarchically optimizes the focalized GP acquisition function over progressively smaller search spaces. Experimental results demonstrate that FocalBO can efficiently leverage large amounts of offline and online data to achieve state-of-the-art performance on robot morphology design and to control a 585-dimensional musculoskeletal system.

DynSyn: Dynamical Synergistic Representation for Efficient Learning and Control in Overactuated Embodied Systems

Learning an effective policy to control high-dimensional, overactuated systems is a significant challenge for deep reinforcement learning algorithms. Such control scenarios are often observed in the neural control of vertebrate musculoskeletal systems. The study of these control mechanisms will provide insights into the control of high-dimensional, overactuated systems. The coordination of actuators, known as muscle synergies in neuromechanics, is considered a presumptive mechanism that simplifies the generation of motor commands. The dynamical structure of a system is the basis of its function, allowing us to derive a synergistic representation of actuators. Motivated by this theory, we propose the Dynamical Synergistic Representation (DynSyn) algorithm. DynSyn aims to generate synergistic representations from dynamical structures and perform task-specific, state-dependent adaptation to the representations to improve motor control. We demonstrate DynSyn's efficiency across various tasks involving different musculoskeletal models, achieving state-of-the-art sample efficiency and robustness compared to baseline algorithms. DynSyn generates interpretable synergistic representations that capture the essential features of dynamical structures and demonstrates generalizability across diverse motor tasks.

Distributionally Robust Constrained Reinforcement Learning under Strong Duality

We study the problem of Distributionally Robust Constrained RL (DRC-RL), where the goal is to maximize the expected reward subject to environmental distribution shifts and constraints. This setting captures situations where training and testing environments differ, and policies must satisfy constraints motivated by safety or limited budgets. Despite significant progress toward algorithm design for the separate problems of distributionally robust RL and constrained RL, there do not yet exist algorithms with end-to-end convergence guarantees for DRC-RL. We develop an algorithmic framework based on strong duality that enables the first efficient and provable solution in a class of environmental uncertainties. Further, our framework exposes an inherent structure of DRC-RL that arises from the combination of distributional robustness and constraints, which prevents a popular class of iterative methods from tractably solving DRC-RL, despite such frameworks being applicable for each of distributionally robust RL and constrained RL individually. Finally, we conduct experiments on a car racing benchmark to evaluate the effectiveness of the proposed algorithm.

A Survey of Constraint Formulations in Safe Reinforcement Learning

Ensuring safety is critical when applying reinforcement learning (RL) to real-world problems. Consequently, safe RL emerges as a fundamental and powerful paradigm for safely optimizing an agent's policy from experimental data. A popular safe RL approach is based on a constrained criterion, which solves the problem of maximizing expected cumulative reward under safety constraints. Though there has been recently a surge of such attempts to achieve safety in RL, a systematic understanding of the field is difficult due to 1) the diversity of constraint representations and 2) little discussion of their interrelations. To address this knowledge gap, we provide a comprehensive review of representative constraint formulations, along with a curated selection of algorithms specifically designed for each formulation. Furthermore, we elucidate the theoretical underpinnings that reveal the mathematical mutual relations among common problem formulations. We conclude with a discussion of the current state and future directions of safe reinforcement learning research.

Improving sample efficiency of high dimensional Bayesian optimization with MCMC

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking Gaussian process posteriors and need to partition the optimization problem into small regions to ensure exploration or assume an underlying low-dimensional structure. With the idea of transiting the candidate points towards more promising positions, we propose a new method based on Markov Chain Monte Carlo to efficiently sample from an approximated posterior. We provide theoretical guarantees of its convergence in the Gaussian process Thompson sampling setting. We also show experimentally that both the Metropolis-Hastings and the Langevin Dynamics version of our algorithm outperform state-of-the-art methods in high-dimensional sequential optimization and reinforcement learning benchmarks.

An Invariant Information Geometric Method for High-Dimensional Online Optimization

Sample efficiency is crucial in optimization, particularly in black-box scenarios characterized by expensive evaluations and zeroth-order feedback. When computing resources are plentiful, Bayesian optimization is often favored over evolution strategies. In this paper, we introduce a full invariance oriented evolution strategies algorithm, derived from its corresponding framework, that effectively rivals the leading Bayesian optimization method in tasks with dimensions at the upper limit of Bayesian capability. Specifically, we first build the framework InvIGO that fully incorporates historical information while retaining the full invariant and computational complexity. We then exemplify InvIGO on multi-dimensional Gaussian, which gives an invariant and scalable optimizer SynCMA . The theoretical behavior and advantages of our algorithm over other Gaussian-based evolution strategies are further analyzed. Finally, We benchmark SynCMA against leading algorithms in Bayesian optimization and evolution strategies on various high dimension tasks, in cluding Mujoco locomotion tasks, rover planning task and synthetic functions. In all scenarios, SynCMA demonstrates great competence, if not dominance, over other algorithms in sample efficiency, showing the underdeveloped potential of property oriented evolution strategies.

Self Model for Embodied Intelligence: Modeling Full-Body Human Musculoskeletal System and Locomotion Control with Hierarchical Low-Dimensional Representation

Modeling and control of the human musculoskeletal system is important for understanding human motion, developing embodied intelligence, and optimizing human-robot interaction systems. However, current open-source models are restricted to a limited range of body parts and often with a reduced number of muscles. There is also a lack of algorithms capable of controlling over 600 muscles to generate reasonable human movements. To fill this gap, we build a comprehensive musculoskeletal model with 90 body segments, 206 joints, and 700 muscle-tendon units, allowing simulation of full-body dynamics and interaction with various devices. We develop a new algorithm using low-dimensional representation and hierarchical deep reinforcement learning to achieve state-of-the-art full-body control. We validate the effectiveness of our model and algorithm in simulations and on real human locomotion data. The musculoskeletal model, along with its control algorithm, will be made available to the research community to promote a deeper understanding of human motion control and better design of interactive robots.

Automatic Sleep Stage Classification with Cross-modal Self-supervised Features from Deep Brain Signals

The detection of human sleep stages is widely used in the diagnosis and intervention of neurological and psychiatric diseases. Some patients with deep brain stimulator implanted could have their neural activities recorded from the deep brain. Sleep stage classification based on deep brain recording has great potential to provide more precise treatment for patients. The accuracy and generalizability of existing sleep stage classifiers based on local field potentials are still limited. We proposed an applicable cross-modal transfer learning method for sleep stage classification with implanted devices. This end-to-end deep learning model contained cross-modal self-supervised feature representation, self-attention, and classification framework. We tested the model with deep brain recording data from 12 patients with Parkinson's disease. The best total accuracy reached 83.2% for sleep stage classification. Results showed speech self-supervised features catch the conversion pattern of sleep stages effectively. We provide a new method on transfer learning from acoustic signals to local field potentials. This method supports an effective solution for the insufficient scale of clinical data. This sleep stage classification model could be adapted to chronic and continuous monitor sleep for Parkinson's patients in daily life, and potentially utilized for more precise treatment in deep brain-machine interfaces, such as closed-loop deep brain stimulation.

Safe Policy Optimization with Local Generalized Linear Function Approximations

Safe exploration is a key to applying reinforcement learning (RL) in safety-critical systems. Existing safe exploration methods guaranteed safety under the assumption of regularity, and it has been difficult to apply them to large-scale real problems. We propose a novel algorithm, SPO-LF, that optimizes an agent's policy while learning the relation between a locally available feature obtained by sensors and environmental reward/safety using generalized linear function approximations. We provide theoretical guarantees on its safety and optimality. We experimentally show that our algorithm is 1) more efficient in terms of sample complexity and computational cost and 2) more applicable to large-scale problems than previous safe RL methods with theoretical guarantees, and 3) comparably sample-efficient and safer compared with existing advanced deep RL methods with safety constraints.