In this study, we consider the infinite-horizon, discounted cost, optimal control of stochastic nonlinear systems with separable cost and constraints in the state and input variables. Using the linear-time Legendre transform, we propose a novel numerical scheme for implementation of the corresponding value iteration (VI) algorithm in the conjugate domain. Detailed analyses of the convergence, time complexity, and error of the proposed algorithm are provided. In particular, with a discretization of size X and U for the state and input spaces, respectively, the proposed approach reduces the time complexity of each iteration in the VI algorithm from O(XU) to O(X U), by replacing the minimization operation in the primal domain with a simple addition in the conjugate domain.

Offline Reinforcement Learning (Offline RL) presents challenges of learning effective decision-making policies from static datasets without any online interactions. Data augmentation techniques, such as noise injection and data synthesizing, aim to improve Q-function approximation by smoothing the learned state-action region. However, these methods often fall short of directly improving the quality of offline datasets, leading to suboptimal results. In response, we introduce GTA, Generative Trajectory Augmentation, a novel generative data augmentation approach designed to enrich offline data by augmenting trajectories to be both high-rewarding and dynamically plausible. GTA applies a diffusion model within the data augmentation framework.

One of the fundamental challenges for offline reinforcement learning (RL) is ensuring robustness to data distribution. Whether the data originates from a near-optimal policy or not, we anticipate that an algorithm should demonstrate its ability to learn an effective control policy that seamlessly aligns with the inherent distribution of offline data. Unfortunately, behavior regularization, a simple yet effective offline RL algorithm, tends to struggle in this regard. In this paper, we propose a new algorithm that substantially enhances behavior-regularization based on conservative policy iteration. Our key observation is that by iteratively refining the reference policy used for behavior regularization, conservative policy update guarantees gradually improvement, while also implicitly avoiding querying out-of-sample actions to prevent catastrophic learning failures.

Existing Maximum-Entropy (MaxEnt) Reinforcement Learning (RL) methods for continuous action spaces are typically formulated based on actor-critic frameworks and optimized through alternating steps of policy evaluation and policy improvement. In the policy evaluation steps, the critic is updated to capture the soft Q-function. In the policy improvement steps, the actor is adjusted in accordance with the updated soft Q-function. In this paper, we introduce a new MaxEnt RL framework modeled using Energy-Based Normalizing Flows (EBFlow). Our method enables the calculation of the soft value function used in the policy evaluation target without Monte Carlo approximation.

In online Inverse Reinforcement Learning (IRL), the learner can collect samples about the dynamics of the environment to improve itsestimate of the reward function. Since IRL suffers from identifiability issues, many theoretical works on online IRL focus on estimating the entire set of rewards that explain the demonstrations, named the feasible reward set. However, none of the algorithms available in literature can scale to problems with large state spaces. In this paper, we focus on the online IRL problem in Linear Markov DecisionProcesses (MDPs). We show that the structure offered by Linear MDPs is not sufficient for efficiently estimating the feasible set when the state space is large.

Designing generalizable agents capable of adapting to diverse embodiments has achieved significant attention in Reinforcement Learning (RL), which is critical for deploying RL agents in various real-world applications. Previous Cross-Embodiment RL approaches have focused on transferring knowledge across embodiments within specific tasks. These methods often result in knowledge tightly coupled with those tasks and fail to adequately capture the distinct characteristics of different embodiments. To address this limitation, we introduce the notion of Cross-Embodiment Unsupervised RL (CEURL), which leverages unsupervised learning to enable agents to acquire embodiment-aware and task-agnostic knowledge through online interactions within reward-free environments. We formulate CEURL as a novel Controlled Embodiment Markov Decision Process (CE-MDP) and systematically analyze CEURL's pre-training objectives under CE-MDP.

Distribution shift'' is the primary obstacle to the success of offline reinforcement learning. As a learning policy may take actions beyond the knowledge of the behavior policy (referred to as Out-of-Distribution (OOD) actions), the Q-values of these OOD actions can be easily overestimated. Consequently, the learning policy becomes biasedly optimized using the incorrect recovered Q-value function. One commonly used idea to avoid the overestimation of Q-value is to make a pessimistic adjustment. Our key idea is to penalize the Q-values of OOD actions that correspond to high uncertainty.

In environments with delayed observation, state augmentation by including actions within the delay window is adopted to retrieve Markovian property to enable reinforcement learning (RL). Whereas, state-of-the-art (SOTA) RL techniques with Temporal-Difference (TD) learning frameworks commonly suffer from learning inefficiency, due to the significant expansion of the augmented state space with the delay. To improve the learning efficiency without sacrificing performance, this work novelly introduces Variational Delayed Policy Optimization (VDPO), reforming delayed RL as a variational inference problem. This problem is further modelled as a two-step iterative optimization problem, where the first step is TD learning in the delay-free environment with a small state space, and the second step is behaviour cloning which can be addressed much more efficiently than TD learning. We not only provide a theoretical analysis of VDPO in terms of sample complexity and performance, but also empirically demonstrate that VDPO can achieve consistent performance with SOTA methods, with a significant enhancement of sample efficiency (approximately 50\% less amount of samples) in the MuJoCo benchmark.

Reinforcement learning (RL) has proven highly effective in addressing complex decision-making and control tasks. However, in most traditional RL algorithms, the policy is typically parameterized as a diagonal Gaussian distribution with learned mean and variance, which constrains their capability to acquire complex policies. In response to this problem, we propose an online RL algorithm termed diffusion actor-critic with entropy regulator (DACER). This algorithm conceptualizes the reverse process of the diffusion model as a novel policy function and leverages the capability of the diffusion model to fit multimodal distributions, thereby enhancing the representational capacity of the policy. Since the distribution of the diffusion policy lacks an analytical expression, its entropy cannot be determined analytically.

Diffusion models have garnered widespread attention in Reinforcement Learning (RL) for their powerful expressiveness and multimodality. It has been verified that utilizing diffusion policies can significantly improve the performance of RL algorithms in continuous control tasks by overcoming the limitations of unimodal policies, such as Gaussian policies. Furthermore, the multimodality of diffusion policies also shows the potential of providing the agent with enhanced exploration capabilities. However, existing works mainly focus on applying diffusion policies in offline RL, while their incorporation into online RL has been less investigated. The diffusion model's training objective, known as the variational lower bound, cannot be applied directly in online RL due to the unavailability of'good' samples (actions).