Qiang HE

Representation rank is an important concept for understanding the role of Neural Networks (NNs) in Deep Reinforcement learning (DRL), which measures the expressive capacity of value networks. Existing studies focus on unboundedly maximizing this rank; nevertheless, that approach would introduce overly complex models in the learning, thus undermining performance. Hence, fine-tuning representation rank presents a challenging and crucial optimization problem. To address this issue, we find a guiding principle for adaptive control of the representation rank. We employ the Bellman equation as a theoretical foundation and derive an upper bound on the cosine similarity of consecutive state-action pairs representations of value networks. We then leverage this upper bound to propose a novel regularizer, namely BEllman Equation-based automatic rank Regularizer (BEER). This regularizer adaptively regularizes the representation rank, thus improving the DRL agent’s performance. We first validate the effectiveness of automatic control of rank on illustrative experiments. Then, we scale up BEER to complex continuous control tasks by combining it with the deterministic policy gradient method. Among 12 challenging DeepMind control tasks, BEER outperforms the baselines by a large margin. Besides, BEER demonstrates significant advantages in Q-value approximation. Our anonymous code is available at https://anonymous.4open.science/r/BEER-3C4B.

Unsupervised reinforcement learning (URL) aims to learn general skills for unseen downstream tasks. Mutual Information Skill Learning (MISL) addresses URL by maximizing the mutual information between states and skills but lacks sufficient theoretical analysis, e.g., how well its learned skills can initialize a downstream task’s policy. Our new theoretical analysis shows that the diversity and separatability of learned skills are fundamentally critical to downstream task adaptation but MISL does not necessarily guarantee them. To improve MISL, we propose a novel disentanglement metric LSEPIN and build an information-geometric connection between LSEPIN and downstream task adaptation cost. For better geometric properties, we investigate a new strategy that replaces the KL divergence in information geometry with Wasserstein distance. We extend the geometric analysis to it, which leads to a novel skill-learning objective WSEP. It is theoretically justified to be helpful to task adaptation and it is capable of discovering more initial policies for downstream tasks than MISL. We further propose a Wasserstein distance-based algorithm PWSEP can theoretically discover all potentially optimal initial policies.

The combination of deep reinforcement learning (DRL) with ensemble methods has been proved to be highly effective in addressing complex sequential decision-making problems. This success can be primarily attributed to the utilization of multiple models, which enhances both the robustness of the policy and the accuracy of value function estimation. However, there has been limited analysis of the empirical success of current ensemble RL methods thus far. Our new analysis reveals that the sample efficiency of previous ensemble DRL algorithms may be limited by sub-policies that are not as diverse as they could be. Motivated by these findings, our study introduces a new ensemble RL algorithm, termed \textbfTrajectories-awar\textbfE \textbfEnsemble exploratio\textbfN (TEEN). The primary goal of TEEN is to maximize the expected return while promoting more diverse trajectories. Through extensive experiments, we demonstrate that TEEN not only enhances the sample diversity of the ensemble policy compared to using sub-policies alone but also improves the performance over ensemble RL algorithms. On average, TEEN outperforms the baseline ensemble DRL algorithms by 41% in performance on the tested representative environments.

We propose a novel value approximation method, namely Eigensubspace Regularized Critic (ERC) for deep reinforcement learning (RL). ERC is motivated by an analysis of the dynamics of Q-value approximation error in the Temporal-Difference (TD) method, which follows a path defined by the 1-eigensubspace of the transition kernel associated with the Markov Decision Process (MDP). It reveals a fundamental property of TD learning that has remained unused in previous deep RL approaches. In ERC, we propose a regularizer that guides the approximation error tending towards the 1-eigensubspace, resulting in a more efficient and stable path of value approximation. Moreover, we theoretically prove the convergence of the ERC method. Besides, theoretical analysis and experiments demonstrate that ERC effectively reduces the variance of value functions. Among 26 tasks in the DMControl benchmark, ERC outperforms state-of-the-art methods for 20. Besides, it shows significant advantages in Q-value approximation and variance reduction. Our code is available at this https URL.

Deep reinforcement learning (DRL) gives the promise that an agent learns good policy from high-dimensional information, whereas representation learning removes irrelevant and redundant information and retains pertinent information. In this work, we demonstrate that the learned representation of the Q-network and its target Q-network should, in theory, satisfy a favorable distinguishable representation property. Specifically, there exists an upper bound on the representation similarity of the value functions of two adjacent time steps in a typical DRL setting. However, through illustrative experiments, we show that the learned DRL agent may violate this property and lead to a sub-optimal policy. Therefore, we propose a simple yet effective regularizer called Policy Evaluation with Easy Regularization on Representation (PEER), which aims to maintain the distinguishable representation property via explicit regularization on internal representations. And we provide the convergence rate guarantee of PEER. Implementing PEER requires only one line of code. Our experiments demonstrate that incorporating PEER into DRL can significantly improve performance and sample efficiency. Comprehensive experiments show that PEER achieves state-of-the-art performance on all 4 environments on PyBullet, 9 out of 12 tasks on DMControl, and 19 out of 26 games on Atari. To the best of our knowledge, PEER is the first work to study the inherent representation property of Q-network and its target. Our code is available at this https URL.