Finite-Time Guarantees for Constrained Reinforcement Learning under Partial Observability

This paper addresses the problem of training a reinforcement learning (RL) policy under partial observability by exploiting a privileged, anytime-feasible planner agent available exclusively during training. We formalize this as a Partially Observable Markov Decision Process (POMDP) in which a planner agent with access to an approximate dynamical model and privileged state information guides a learning agent that observes only a lossy projection of the true state. To realize this framework, we introduce an anytime-feasible Model Predictive Control (MPC) algorithm that serves as the planner agent. For the learning agent, we propose Planner-to-Policy Soft Actor-Critic (P2P-SAC), a method that distills the planner agent's privileged knowledge to mitigate partial observability and thereby improve both sample efficiency and final policy performance. We support this framework with rigorous theoretical analysis. Finally, we validate our approach in simulation using NVIDIA Isaac Lab and successfully deploy it on a real-world Unitree Go2 quadruped navigating complex, obstacle-rich environments.

Safety is a fundamental challenge in reinforcement learning (RL), particularly in real-world applications such as autonomous driving, robotics, and healthcare. To address this, Constrained Markov Decision Processes (CMDPs) are commonly used to enforce safety constraints while optimizing performance. However, existing methods often suffer from significant safety violations or require a high sample complexity to generate near-optimal policies. We address two settings: relaxed feasibility, where small violations are allowed, and strict feasibility, where no violation is allowed. We propose a model-based primal-dual algorithm that balances regret and bounded constraint violations, drawing on techniques from online RL and constrained optimization. For relaxed feasibility, we prove that our algorithm returns an $\varepsilon$-optimal policy with $\varepsilon$-bounded violation with arbitrarily high probability, requiring $\tilde{O}\left(\frac{SAH^3}{\varepsilon^2}\right)$ learning episodes, matching the lower bound for unconstrained MDPs. For strict feasibility, we prove that our algorithm returns an $\varepsilon$-optimal policy with zero violation with arbitrarily high probability, requiring $\tilde{O}\left(\frac{SAH^5}{\varepsilon^2ζ^2}\right)$ learning episodes, where $ζ$ is the problem-dependent Slater constant characterizing the size of the feasible region. This result matches the lower bound for learning CMDPs with access to a generative model. Our results demonstrate that learning CMDPs in an online setting is as easy as learning with a generative model and is no more challenging than learning unconstrained MDPs when small violations are allowed.

We study model-based learning of finite-window policies in tabular partially observable Markov decision processes (POMDPs). A common approach to learning under partial observability is to approximate unbounded history dependencies using finite action-observation windows. This induces a finite-state Markov decision process (MDP) over histories, referred to as the superstate MDP. Once a model of this superstate MDP is available, standard MDP algorithms can be used to compute optimal policies, motivating the need for sample-efficient model estimation. Estimating the superstate MDP model is challenging because trajectories are generated by interaction with the original POMDP, creating a mismatch between the sampling process and target model. We propose a model estimation procedure for tabular POMDPs and analyze its sample complexity. Our analysis exploits a connection between filter stability and concentration inequalities for weakly dependent random variables. As a result, we obtain tight sample complexity guarantees for estimating the superstate MDP model from a single trajectory. Combined with value iteration, this yields approximately optimal finite-window policies for the POMDP.