Entropy-based objectives are widely used to perform state space exploration in reinforcement learning (RL) and dataset generation for offline RL. Behavioral entropy (BE), a rigorous generalization of classical entropies that incorporates cognitive and perceptual biases of agents, was recently proposed for discrete settings and shown to be a promising metric for robotic exploration problems. In this work, we propose using BE as a principled exploration objective for systematically generating datasets that provide diverse state space coverage in complex, continuous, potentially high-dimensional domains. To achieve this, we extend the notion of BE to continuous settings, derive tractable $k$-nearest neighbor estimators, provide theoretical guarantees for these estimators, and develop practical reward functions that can be used with standard RL methods to learn BE-maximizing policies. Using standard MuJoCo environments, we experimentally compare the performance of offline RL algorithms for a variety of downstream tasks on datasets generated using BE, R\'{e}nyi, and Shannon entropy-maximizing policies, as well as the SMM and RND algorithms. We find that offline RL algorithms trained on datasets collected using BE outperform those trained on datasets collected using Shannon entropy, SMM, and RND on all tasks considered, and on 80\% of the tasks compared to datasets collected using Renyi entropy.

Reinforcement learning (RL) is a promising approach for robotic navigation, allowing robots to learn through trial and error. However, real-world robotic tasks often suffer from sparse rewards, leading to inefficient exploration and suboptimal policies due to sample inefficiency of RL. In this work, we introduce Confidence-Controlled Exploration (CCE), a novel method that improves sample efficiency in RL-based robotic navigation without modifying the reward function. Unlike existing approaches, such as entropy regularization and reward shaping, which can introduce instability by altering rewards, CCE dynamically adjusts trajectory length based on policy entropy. Specifically, it shortens trajectories when uncertainty is high to enhance exploration and extends them when confidence is high to prioritize exploitation. CCE is a principled and practical solution inspired by a theoretical connection between policy entropy and gradient estimation. It integrates seamlessly with on-policy and off-policy RL methods and requires minimal modifications. We validate CCE across REINFORCE, PPO, and SAC in both simulated and real-world navigation tasks. CCE outperforms fixed-trajectory and entropy-regularized baselines, achieving an 18% higher success rate, 20-38% shorter paths, and 9.32% lower elevation costs under a fixed training sample budget. Finally, we deploy CCE on a Clearpath Husky robot, demonstrating its effectiveness in complex outdoor environments.

Estimating nonlinear functionals of probability densities is an important problem in a variety of domains. The family of k-nearest neighbor density functional estimators provides simple, effective tools for achieving this. In this paper we provide finite-sample analysis of both plug-in and bias-corrected fixed-k k-nearest neighbor estimators of nonlinear density functionals.

We develop policy gradient algorithms with global optimality and convergence guarantees for reinforcement learning (RL) with proportional-integral-derivative (PID) parameterized control policies. RL enables learning control policies through direct interaction with a system, without explicit model knowledge that is typically assumed in classical control. The PID policy architecture offers built-in structural advantages, such as superior tracking performance, elimination of steady-state errors, and robustness to model error that have made it a widely adopted paradigm in practice. Despite these advantages, the PID parameterization has received limited attention in the RL literature, and PID control designs continue to rely on heuristic tuning rules without theoretical guarantees. We address this gap by rigorously integrating PID control with RL, offering theoretical guarantees while maintaining the practical advantages that have made PID control ubiquitous in practice. Specifically, we first formulate PID control design as an optimization problem with a control policy that is parameterized by proportional, integral, and derivative components. We derive exact expressions for policy gradients in these parameters, and leverage them to develop both model-based and model-free policy gradient algorithms for PID policies. We then establish gradient dominance properties of the PID policy optimization problem, and provide theoretical guarantees on convergence and global optimality in this setting. Finally, we benchmark the performance of our algorithms on the controlgym suite of environments.

We develop provably safe and convergent reinforcement learning (RL) algorithms for control of nonlinear dynamical systems, bridging the gap between the hard safety guarantees of control theory and the convergence guarantees of RL theory. Recent advances at the intersection of control and RL follow a two-stage, safety filter approach to enforcing hard safety constraints: model-free RL is used to learn a potentially unsafe controller, whose actions are projected onto safe sets prescribed, for example, by a control barrier function. Though safe, such approaches lose any convergence guarantees enjoyed by the underlying RL methods. In this paper, we develop a single-stage, sampling-based approach to hard constraint satisfaction that learns RL controllers enjoying classical convergence guarantees while satisfying hard safety constraints throughout training and deployment. We validate the efficacy of our approach in simulation, including safe control of a quadcopter in a challenging obstacle avoidance problem, and demonstrate that it outperforms existing benchmarks.

In the context of average-reward reinforcement learning, the requirement for oracle knowledge of the mixing time, a measure of the duration a Markov chain under a fixed policy needs to achieve its stationary distribution, poses a significant challenge for the global convergence of policy gradient methods. This requirement is particularly problematic due to the difficulty and expense of estimating mixing time in environments with large state spaces, leading to the necessity of impractically long trajectories for effective gradient estimation in practical applications. To address this limitation, we consider the Multi-level Actor-Critic (MAC) framework, which incorporates a Multi-level Monte-Carlo (MLMC) gradient estimator. With our approach, we effectively alleviate the dependency on mixing time knowledge, a first for average-reward MDPs global convergence. Furthermore, our approach exhibits the tightest available dependence of $\mathcal{O}(\sqrt{\tau_{mix}})$ known from prior work. With a 2D grid world goal-reaching navigation experiment, we demonstrate that MAC outperforms the existing state-of-the-art policy gradient-based method for average reward settings.

In this work, we introduce PIPER: Primitive-Informed Preference-based Hierarchical reinforcement learning via Hindsight Relabeling, a novel approach that leverages preference-based learning to learn a reward model, and subsequently uses this reward model to relabel higher-level replay buffers. Since this reward is unaffected by lower primitive behavior, our relabeling-based approach is able to mitigate non-stationarity, which is common in existing hierarchical approaches, and demonstrates impressive performance across a range of challenging sparse-reward tasks. Since obtaining human feedback is typically impractical, we propose to replace the human-in-the-loop approach with our primitive-in-the-loop approach, which generates feedback using sparse rewards provided by the environment. Moreover, in order to prevent infeasible subgoal prediction and avoid degenerate solutions, we propose primitive-informed regularization that conditions higher-level policies to generate feasible subgoals for lower-level policies. We perform extensive experiments to show that PIPER mitigates non-stationarity in hierarchical reinforcement learning and achieves greater than 50$\%$ success rates in challenging, sparse-reward robotic environments, where most other baselines fail to achieve any significant progress.

Navigating robots through unstructured terrains is challenging, primarily due to the dynamic environmental changes. While humans adeptly navigate such terrains by using context from their observations, creating a similar context-aware navigation system for robots is difficult. The essence of the issue lies in the acquisition and interpretation of context information, a task complicated by the inherent ambiguity of human language. In this work, we introduce LANCAR, which addresses this issue by combining a context translator with reinforcement learning (RL) agents for context-aware locomotion. LANCAR allows robots to comprehend context information through Large Language Models (LLMs) sourced from human observers and convert this information into actionable context embeddings. These embeddings, combined with the robot’s sensor data, provide a complete input for the RL agent’s policy network. We provide an extensive evaluation of LANCAR under different levels of context ambiguity and compare with alternative methods. The experimental results showcase the superior generalizability and adaptability across different terrains. Notably, LANCAR shows at least a 7.4% increase in episodic reward over the best alternatives, highlighting its potential to enhance robotic navigation in unstructured environments. More details and experiment videos could be found in this link.

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call Multi-level Actor-Critic (MAC), is developed specifically for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it is therefore readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to SOTA actor-critic algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.

Ratio maximization has applications in areas as diverse as finance, reward shaping for reinforcement learning (RL), and the development of safe artificial intelligence, yet there has been very little exploration of RL algorithms for ratio maximization. This paper addresses this deficiency by introducing two new, model-free RL algorithms for solving cost-aware Markov decision processes, where the goal is to maximize the ratio of long-run average reward to long-run average cost. The first algorithm is a two-timescale scheme based on relative value iteration (RVI) Q-learning and the second is an actor-critic scheme. The paper proves almost sure convergence of the former to the globally optimal solution in the tabular case and almost sure convergence of the latter under linear function approximation for the critic. Unlike previous methods, the two algorithms provably converge for general reward and cost functions under suitable conditions. The paper also provides empirical results demonstrating promising performance and lending strong support to the theoretical results.