Adaptive Regularization of Representation Rank as an Implicit Constraint of Bellman Equation

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 code is available at https://github.com/sweetice/BEER-ICLR2024.

Keep Various Trajectories: Promoting Exploration of Ensemble Policies in Continuous Control

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 \textbf{T}rajectories-awar\textbf{E} \textbf{E}nsemble exploratio\textbf{N} (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.

Self-supervised Noise2noise Method Utilizing Corrupted Images with a Modular Network for LDCT Denoising

Deep learning is a very promising technique for low-dose computed tomography (LDCT) image denoising. However, traditional deep learning methods require paired noisy and clean datasets, which are often difficult to obtain. This paper proposes a new method for performing LDCT image denoising with only LDCT data, which means that normal-dose CT (NDCT) is not needed. We adopt a combination including the self-supervised noise2noise model and the noisy-as-clean strategy. First, we add a second yet similar type of noise to LDCT images multiple times. Note that we use LDCT images based on the noisy-as-clean strategy for corruption instead of NDCT images. Then, the noise2noise model is executed with only the secondary corrupted images for training. We select a modular U-Net structure from several candidates with shared parameters to perform the task, which increases the receptive field without increasing the parameter size. The experimental results obtained on the Mayo LDCT dataset show the effectiveness of the proposed method compared with that of state-of-the-art deep learning methods. The developed code is available at https://github.com/XYuan01/Self-supervised-Noise2Noise-for-LDCT.

Eigensubspace of Temporal-Difference Dynamics and How It Improves Value Approximation in Reinforcement Learning

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 https://sites.google.com/view/erc-ecml23/.

Centralized Cooperative Exploration Policy for Continuous Control Tasks

The deep reinforcement learning (DRL) algorithm works brilliantly on solving various complex control tasks. This phenomenal success can be partly attributed to DRL encouraging intelligent agents to sufficiently explore the environment and collect diverse experiences during the agent training process. Therefore, exploration plays a significant role in accessing an optimal policy for DRL. Despite recent works making great progress in continuous control tasks, exploration in these tasks has remained insufficiently investigated. To explicitly encourage exploration in continuous control tasks, we propose CCEP (Centralized Cooperative Exploration Policy), which utilizes underestimation and overestimation of value functions to maintain the capacity of exploration. CCEP first keeps two value functions initialized with different parameters, and generates diverse policies with multiple exploration styles from a pair of value functions. In addition, a centralized policy framework ensures that CCEP achieves message delivery between multiple policies, furthermore contributing to exploring the environment cooperatively. Extensive experimental results demonstrate that CCEP achieves higher exploration capacity. Empirical analysis shows diverse exploration styles in the learned policies by CCEP, reaping benefits in more exploration regions. And this exploration capacity of CCEP ensures it outperforms the current state-of-the-art methods across multiple continuous control tasks shown in experiments.

Adaptive Weighted Nonnegative Matrix Factorization for Robust Feature Representation

Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the robustness of NMF, this paper proposes an adaptive weighted NMF, which introduces weights to emphasize the different importance of each data point, thus the algorithmic sensitivity to noisy data is decreased. It is very different from the existing robust NMFs that use a slow growth similarity measure. Specifically, two strategies are proposed to achieve this: fuzzier weighted technique and entropy weighted regularized technique, and both of them lead to an iterative solution with a simple form. Experimental results showed that new methods have more robust feature representation on several real datasets with noise than exsiting methods.

Representation Gap in Deep Reinforcement Learning

Deep reinforcement learning 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. We consider the representation capacity of action value function and theoretically reveal its inherent property, \textit{representation gap} with its target action value function. This representation gap is favorable. However, through illustrative experiments, we show that the representation of action value function grows similarly compared with its target value function, i.e. the undesirable inactivity of the representation gap (\textit{representation overlap}). Representation overlap results in a loss of representation capacity, which further leads to sub-optimal learning performance. To activate the representation gap, we propose a simple but effective framework \underline{P}olicy \underline{O}ptimization from \underline{P}reventing \underline{R}epresentation \underline{O}verlaps (POPRO), which regularizes the policy evaluation phase through differing the representation of action value function from its target. We also provide the convergence rate guarantee of POPRO. We evaluate POPRO on gym continuous control suites. The empirical results show that POPRO using pixel inputs outperforms or parallels the sample-efficiency of methods that use state-based features.

Improving the Level of Autism Discrimination through GraphRNN Link Prediction

Dataset is the key of deep learning in Autism disease research. However, due to the few quantity and heterogeneity of samples in current dataset, for example ABIDE (Autism Brain Imaging Data Exchange), the recognition research is not effective enough. Previous studies mostly focused on optimizing feature selection methods and data reinforcement to improve accuracy. This paper is based on the latter technique, which learns the edge distribution of real brain network through GraphRNN, and generates the synthetic data which has incentive effect on the discriminant model. The experimental results show that the combination of original and synthetic data greatly improves the discrimination of the neural network. For instance, the most significant effect is the 50-layer ResNet, and the best generation model is GraphRNN, which improves the accuracy by 32.51% compared with the model reference experiment without generation data reinforcement. Because the generated data comes from the learned edge connection distribution of Autism patients and typical controls functional connectivity, but it has better effect than the original data, which has constructive significance for further understanding of disease mechanism and development.

An Entropy Weighted Nonnegative Matrix Factorization Algorithm for Feature Representation

Nonnegative matrix factorization (NMF) has been widely used to learn low-dimensional representations of data. However, NMF pays the same attention to all attributes of a data point, which inevitably leads to inaccurate representation. For example, in a human-face data set, if an image contains a hat on the head, the hat should be removed or the importance of its corresponding attributes should be decreased during matrix factorizing. This paper proposes a new type of NMF called entropy weighted NMF (EWNMF), which uses an optimizable weight for each attribute of each data point to emphasize their importance. This process is achieved by adding an entropy regularizer to the cost function and then using the Lagrange multiplier method to solve the problem. Experimental results with several data sets demonstrate the feasibility and effectiveness of the proposed method. We make our code available at https://github.com/Poisson-EM/Entropy-weighted-NMF.

Combing Policy Evaluation and Policy Improvement in a Unified f-Divergence Framework

The framework of deep reinforcement learning (DRL) provides a powerful and widely applicable mathematical formalization for sequential decision-making. In this paper, we start from studying the f-divergence between learning policy and sampling policy and derive a novel DRL framework, termed f-Divergence Reinforcement Learning (FRL). We highlight that the policy evaluation and policy improvement phases are induced by minimizing f-divergence between learning policy and sampling policy, which is distinct from the conventional DRL algorithm objective that maximizes the expected cumulative rewards. Besides, we convert this framework to a saddle-point optimization problem with a specific f function through Fenchel conjugate, which consists of policy evaluation and policy improvement. Then we derive new policy evaluation and policy improvement methods in FRL. Our framework may give new insights for analyzing DRL algorithms. The FRL framework achieves two advantages: (1) policy evaluation and policy improvement processes are derived simultaneously by f-divergence; (2) overestimation issue of value function are alleviated. To evaluate the effectiveness of the FRL framework, we conduct experiments on Atari 2600 video games, which show that our framework matches or surpasses the DRL algorithms we tested.