While machine learning can myopically reinforce social inequalities, it may also be used to dynamically seek equitable outcomes.

We propose a Bayesian decision making framework for control of Markov Decision Processes (MDPs) with unknown dynamics and large, possibly continuous, state, action, and parameter spaces in data-poor environments. Most of the existing adaptive controllers for MDPs with unknown dynamics are based on the reinforcement learning framework and rely on large data sets acquired by sustained direct interaction with the system or via a simulator. This is not feasible in many applications, due to ethical, economic, and physical constraints. The proposed framework addresses the data poverty issue by decomposing the problem into an offline planning stage that does not rely on sustained direct interaction with the system or simulator and an online execution stage. In the offline process, parallel Gaussian process temporal difference (GPTD) learning techniques are employed for near-optimal Bayesian approximation of the expected discounted reward over a sample drawn from the prior distribution of unknown parameters. In the online stage, the action with the maximum expected return with respect to the posterior distribution of the parameters is selected. This is achieved by an approximation of the posterior distribution using a Markov Chain Monte Carlo (MCMC) algorithm, followed by constructing multiple Gaussian processes over the parameter space for efficient prediction of the means of the expected return at the MCMC sample. The effectiveness of the proposed framework is demonstrated using a simple dynamical system model with continuous state and action spaces, as well as a more complex model for a metastatic melanoma gene regulatory network observed through noisy synthetic gene expression data.

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We present a policy search method that uses iteratively refitted local linear models to optimize trajectory distributions for large, continuous problems. These trajectory distributions can be used within the framework of guided policy search to learn policies with an arbitrary parameterization. Our method fits time-varying linear dynamics models to speed up learning, but does not rely on learning a global model, which can be difficult when the dynamics are complex and discontinuous. We show that this hybrid approach requires many fewer samples than model-free methods, and can handle complex, nonsmooth dynamics that can pose a challenge for model-based techniques. We present experiments showing that our method can be used to learn complex neural network policies that successfully execute simulated robotic manipulation tasks in partially observed environments with numerous contact discontinuities and underactuation.

Control contraction metrics (CCMs) provide a framework to co-synthesize a controller and a corresponding contraction metric -- a positive-definite Riemannian metric under which a closed-loop system is guaranteed to be incrementally exponentially stable. However, the synthesized controller only ensures that all the trajectories of the system converge to one single trajectory and, as such, does not impose any notion of optimality across an entire trajectory. Furthermore, constructing CCMs requires a known dynamics model and non-trivial effort in solving an infinite-dimensional convex feasibility problem, which limits its scalability to complex systems featuring high dimensionality with uncertainty. To address these issues, we propose to integrate CCMs into reinforcement learning (RL), where CCMs provide dynamics-informed feedback for learning control policies that minimize cumulative tracking error under unknown dynamics. We show that our algorithm, called contraction actor-critic (CAC), formally enhances the capability of CCMs to provide a set of contracting policies with the long-term optimality of RL in a fully automated setting. Given a pre-trained dynamics model, CAC simultaneously learns a contraction metric generator (CMG) -- which generates a contraction metric -- and uses an actor-critic algorithm to learn an optimal tracking policy guided by that metric. We demonstrate the effectiveness of our algorithm relative to established baselines through extensive empirical studies, including simulated and real-world robot experiments, and provide a theoretical rationale for incorporating contraction theory into RL.

Computationally and Sample Efficient Safe Reinforcement Learning Using Adaptive Conformal Prediction Hao Zhou, Y anze Zhang, and Wenhao Luo Abstract -- Safety is a critical concern in learning-enabled autonomous systems especially when deploying these systems in real-world scenarios. An important challenge is accurately quantifying the uncertainty of unknown models to generate provably safe control policies that facilitate the gathering of informative data, thereby achieving both safe and optimal policies. Additionally, the selection of the data-driven model can significantly impact both the real-time implementation and the uncertainty quantification process. In this paper, we propose a provably sample efficient episodic safe learning framework that remains robust across various model choices with quantified uncertainty for online control tasks. Specifically, we first employ Quadrature Fourier Features (QFF) for kernel function approximation of Gaussian Processes (GPs) to enable efficient approximation of unknown dynamics. Then the Adaptive Conformal Prediction (ACP) is used to quantify the uncertainty from online observations and combined with the Control Barrier Functions (CBF) to characterize the uncertainty-aware safe control constraints under learned dynamics. Finally, an optimism-based exploration strategy is integrated with ACP-based CBFs for safe exploration and near-optimal safe nonlinear control. Theoretical proofs and simulation results are provided to demonstrate the effectiveness and efficiency of the proposed framework. I NTRODUCTION Model-based Reinforcement Learning (MBRL) [1]-[5] has shown promising results when applied to variant nonlinear systems because of its robust generalization capabilities.

Autonomous motion planning under unknown nonlinear dynamics presents significant challenges. An agent needs to continuously explore the system dynamics to acquire its properties, such as reachability, in order to guide system navigation adaptively. In this paper, we propose a hybrid planning-control framework designed to compute a feasible trajectory toward a target. Our approach involves partitioning the state space and approximating the system by a piecewise affine (PWA) system with constrained control inputs. By abstracting the PWA system into a directed weighted graph, we incrementally update the existence of its edges via affine system identification and reach control theory, introducing a predictive reachability condition by exploiting prior information of the unknown dynamics. Heuristic weights are assigned to edges based on whether their existence is certain or remains indeterminate. Consequently, we propose a framework that adaptively collects and analyzes data during mission execution, continually updates the predictive graph, and synthesizes a controller online based on the graph search outcomes. We demonstrate the efficacy of our approach through simulation scenarios involving a mobile robot operating in unknown terrains, with its unknown dynamics abstracted as a single integrator model.

While machine learning can myopically reinforce social inequalities, it may also be used to dynamically seek equitable outcomes. This formulation accommodates dynamical control objectives, such as achieving equitable population states, that cannot be incorporated into static formulations of fairness. We demonstrate that algorithmic solutions to the proposed fairness problem can adapt to unknown dynamics and, by sacrificing short-term incentives, drive the policy-population system towards more desirable equilibria. For the proposed setting, we develop an algorithm that adapts recent work in online learning and prove that this algorithm achieves simultaneous probabilistic bounds on cumulative loss and cumulative violations of fairness. In the classification setting subject to group fairness, we compare our proposed algorithm to several baselines, including the repeated retraining of myopic or distributionally robust classifiers, and to a deep reinforcement learning algorithm that lacks fairness guarantees.

POST-REBUTTAL: Thank you for the clarifications. I've increased the overall score because the rebuttal made me think of this work as an interesting tradeoff between generality and the time when when computational cost investment has to be made (online vs. offline). At the same time, BAMCP has the significant advantage of handling more stochastic (as opposed to nearly deterministic, as in this paper) scenarios, and I would encourage you to work on extending your approach to them. The paper proposes a Bayesian RL method for MDPs with continuous states, action, and parameter spaces. Its key component is efficiently approximating the Q-value function expectations over the posterior belief over the parameter space, which is achieved by a combination of GPTD during the offline stage of the algorithm and MCMC during the online stage.

Model-based controllers using a linearized model around the system's equilibrium point is a common approach in the control of a wheeled humanoid due to their less computational load and ease of stability analysis. However, controlling a wheeled humanoid robot while it lifts an unknown object presents significant challenges, primarily due to the lack of knowledge in object dynamics. This paper presents a framework designed for predicting the new equilibrium point explicitly to control a wheeled-legged robot with unknown dynamics. We estimated the total mass and center of mass of the system from its response to initially unknown dynamics, then calculated the new equilibrium point accordingly. To avoid using additional sensors (e.g., force torque sensor) and reduce the effort of obtaining expensive real data, a data-driven approach is utilized with a novel real-to-sim adaptation. A more accurate nonlinear dynamics model, offering a closer representation of real-world physics, is injected into a rigid-body simulation for real-to-sim adaptation. The nonlinear dynamics model parameters were optimized using Particle Swarm Optimization. The efficacy of this framework was validated on a physical wheeled inverted pendulum, a simplified model of a wheeled-legged robot. The experimental results indicate that employing a more precise analytical model with optimized parameters significantly reduces the gap between simulation and reality, thus improving the efficiency of a model-based controller in controlling a wheeled robot with unknown dynamics.