Recent works in high-dimensional model-predictive control and model-based reinforcement learning with learned dynamics and reward models have resorted to population-based optimization methods, such as the Cross-Entropy Method (CEM), for planning a sequence of actions. To decide on an action to take, CEM conducts a search for the action sequence with the highest return according to the dynamics model and reward. Action sequences are typically randomly sampled from an unconditional Gaussian distribution and evaluated on the environment. This distribution is iteratively updated towards action sequences with higher returns. However, this planning method can be very inefficient, especially for high-dimensional action spaces. An alternative line of approaches optimize action sequences directly via gradient descent, but are prone to local optima. We propose a method to solve this planning problem by interleaving CEM and gradient descent steps in optimizing the action sequence. Our experiments show faster convergence of the proposed hybrid approach, even for high-dimensional action spaces, avoidance of local minima, and better or equal performance to CEM. Code accompanying the paper is available here https://github.com/homangab/gradcem.
Dream-MPC: Gradient-Based Model Predictive Control with Latent Imagination
Autonomous Intelligent Systems, Computer Science Institute VI - Intelligent Systems（自主智能系统，计算机科学研究所VI - 智能系统）；Robotics, Center for Robotics（机器人学，机器人中心）；the Lamarr Institute for Machine Learning（拉马尔机器学习研究所）；Artificial Intelligence, University of Bonn, Germany（人工智能，波恩大学，德国）
Maximum entropy deep reinforcement learning (RL) methods have been demonstrated on a range of challenging continuous tasks. However, existing methods either suffer from severe instability when training on large off-policy data or cannot scale to tasks with very high state and action dimensionality such as 3D humanoid locomotion. Besides, the optimality of desired Boltzmann policy set for non-optimal soft value function is not persuasive enough. In this paper, we first derive soft policy gradient based on entropy regularized expected reward objective for RL with continuous actions. Then, we pre…
Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；Polytechnique Montréal（蒙特利尔理工学院）
Entropy is ubiquitous in machine learning, but it is in general intractable to compute the entropy of the distribution of an arbitrary continuous random variable. In this paper, we propose the amortized residual denoising autoencoder (AR-DAE) to approximate the gradient of the log density function, which can be used to estimate the gradient of entropy. Amortization allows us to significantly reduce the error of the gradient approximator by approaching asymptotic optimality of a regular DAE, in which case the estimation is in theory unbiased. We conduct theoretical and experimental analyses on …
In this paper, a safe and learning-based control framework for model predictive control (MPC) is proposed to optimize nonlinear systems with a non-differentiable objective function under uncertain environmental disturbances. The control framework integrates a learning-based MPC with an auxiliary controller in a way of minimal intervention. The learning-based MPC augments the prior nominal model with incremental Gaussian Processes to learn the uncertain disturbances. The cross-entropy method (CEM) is utilized as the sampling-based optimizer for the MPC with a non-differentiable objective functi…
The policy gradient theorem is defined based on an objective with respect to the initial distribution over states. In the discounted case, this results in policies that are optimal for one distribution over initial states, but may not be uniformly optimal for others, no matter where the agent starts from. Furthermore, to obtain unbiased gradient estimates, the starting point of the policy gradient estimator requires sampling states from a normalized discounted weighting of states. However, the difficulty of estimating the normalized discounted weighting of states, or the stationary state distr…
Carnegie Mellon University（卡内基梅隆大学）；Instituto Superior Técnico（高等技术研究所）；University of Washington（华盛顿大学）
We introduce Recurrent Predictive State Policy (RPSP) networks, a recurrent architecture that brings insights from predictive state representations to reinforcement learning in partially observable environments. Predictive state policy networks consist of a recursive filter, which keeps track of a belief about the state of the environment, and a reactive policy that directly maps beliefs to actions, to maximize the cumulative reward. The recursive filter leverages predictive state representations (PSRs) (Rosencrantz and Gordon, 2004; Sun et al., 2016) by modeling predictive state-- a predictio…
University of Edinburgh（爱丁堡大学）；Imperial College London（帝国理工学院）；Vega Protocol（维加协议）；The Alan Turing Institute（艾伦·图灵研究所）
We study the global convergence of policy gradient for infinite-horizon, continuous state and action space, and entropy-regularized Markov decision processes (MDPs). We consider a softmax policy with (one-hidden layer) neural network approximation in a mean-field regime. Additional entropic regularization in the associated mean-field probability measure is added, and the corresponding gradient flow is studied in the 2-Wasserstein metric. We show that the objective function is increasing along the gradient flow. Further, we prove that if the regularization in terms of the mean-field measure is …
Flexible Entropy Control in RLVR with a Gradient-Preserving Perspective
School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；MAIS, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所MAIS）；Meituan（美团）
Efficient Entropy for Policy Gradient with Multidimensional Action Space
New York University（纽约大学）；New York University Abu Dhabi（纽约大学阿布扎克分校）；New York University Shanghai（纽约大学上海分校）；Massachusetts Institute of Technology（麻省理工学院）
In a reward-free environment, what is a suitable intrinsic objective for an agent to pursue so that it can learn an optimal task-agnostic exploration policy? In this paper, we argue that the entropy of the state distribution induced by finite-horizon trajectories is a sensible target. Especially, we present a novel and practical policy-search algorithm, Maximum Entropy POLicy optimization (MEPOL), to learn a policy that maximizes a non-parametric, $k$-nearest neighbors estimate of the state distribution entropy. In contrast to known methods, MEPOL is completely model-free as it requires neithe…
GMTS: Gradient Magnitude-based Token Selection Improves RLVR Training for LLM Reasoning
School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）
University of Alberta（阿尔伯塔大学）；Alberta Machine Intelligence Institute（阿尔伯塔机器智能研究所）
In computational reinforcement learning, a growing body of work seeks to construct an agent's perception of the world through predictions of future sensations; predictions about environment observations are used as additional input features to enable better goal-directed decision-making. An open challenge in this line of work is determining from the infinitely many predictions that the agent could possibly make which predictions might best support decision-making. This challenge is especially apparent in continual learning problems where a single stream of experience is available to a singular…
Wasserstein Policy Gradient for Entropy-Regularized Linear-Quadratic Control
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Natural policy gradient (NPG) methods are among the most widely used policy optimization algorithms in contemporary reinforcement learning. This class of methods is often applied in conjunction with entropy regularization -- an algorithmic scheme that encourages exploration -- and is closely related to soft policy iteration and trust region policy optimization. Despite the empirical success, the theoretical underpinnings for NPG methods remain limited even for the tabular setting. This paper develops $\textit{non-asymptotic}$ convergence guarantees for entropy-regularized NPG methods under sof…
We present an information theoretic approach to stochastic optimal control problems that can be used to derive general sampling based optimization schemes. This new mathematical method is used to develop a sampling based model predictive control algorithm. We apply this information theoretic model predictive control (IT-MPC) scheme to the task of aggressive autonomous driving around a dirt test track, and compare its performance to a model predictive control version of the cross-entropy method.
Communication in multi-agent reinforcement learning has been drawing attention recently for its significant role in cooperation. However, multi-agent systems may suffer from limitations on communication resources and thus need efficient communication techniques in real-world scenarios. According to the Shannon-Hartley theorem, messages to be transmitted reliably in worse channels require lower entropy. Therefore, we aim to reduce message entropy in multi-agent communication. A fundamental challenge is that the gradients of entropy are either 0 or infinity, disabling gradient-based methods. To …
Real-world reinforcement learning (RL) problems often demand that agents behave safely by obeying a set of designed constraints. We address the challenge of safe RL by coupling a safety guide based on model predictive control (MPC) with a modified policy gradient framework in a linear setting with continuous actions. The guide enforces safe operation of the system by embedding safety requirements as chance constraints in the MPC formulation. The policy gradient training step then includes a safety penalty which trains the base policy to behave safely. We show theoretically that this penalty al…
Global Convergence of Policy Gradient for Entropy Regularized Linear-Quadratic Control with Multiplicative Noise
Department of Mathematics, University of California, Berkeley（加州大学伯克利分校数学系）；College of Computing, Data Science, and Society, University of California, Berkeley（加州大学伯克利分校计算机科学与数据科学学院）；Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）
Entropy-Gradient Inversion: Moving Toward Internal Mechanism of Large Reasoning Models
National University of Singapore（新加坡国立大学）；Renmin University of China（中国人民大学）；Shanghai Jiao Tong University（上海交通大学）；Nanyang Technological University（南洋理工大学）
We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Baye…
We develop parallel predictive entropy search (PPES), a novel algorithm for Bayesian optimization of expensive black-box objective functions. At each iteration, PPES aims to select a batch of points which will maximize the information gain about the global maximizer of the objective. Well known strategies exist for suggesting a single evaluation point based on previous observations, while far fewer are known for selecting batches of points to evaluate in parallel. The few batch selection schemes that have been studied all resort to greedy methods to compute an optimal batch. To the best of our…
Columbia University（哥伦比亚大学）；New York University（纽约大学）
Variational inference transforms posterior inference into parametric optimization thereby enabling the use of latent variable models where otherwise impractical. However, variational inference can be finicky when different variational parameters control variables that are strongly correlated under the model. Traditional natural gradients based on the variational approximation fail to correct for correlations when the approximation is not the true posterior. To address this, we construct a new natural gradient called the Variational Predictive Natural Gradient (VPNG). Unlike traditional natural…
An Innovative Next Activity Prediction Using Process Entropy and Dynamic Attribute-Wise-Transformer in Predictive Business Process Monitoring
Department of Electrical and Computer Engineering, Faculty of Engineering and Computer Science, University of Victoria（维多利亚大学工程与计算机科学学院电气与计算机工程系）；Department of Mechanical Engineering, Faculty of Engineering and Computer Science, University of Victoria（维多利亚大学工程与计算机科学学院机械工程系）
There is an increasing convergence between biologically plausible computational models of inference and learning with local update rules and the global gradient-based optimization of neural network models employed in machine learning. One particularly exciting connection is the correspondence between the locally informed optimization in predictive coding networks and the error backpropagation algorithm that is used to train state-of-the-art deep artificial neural networks. Here we focus on the related, but still largely under-explored connection between precision weighting in predictive coding…
Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we create a convergence condition to build a learning rate which varies adaptively with local smoothness. Second, the local smoothness can be predicted by the latest gradients. Third, we use the adaptive learning rate to update the stochastic gradients for exploring linear convergen…
A Hierarchy of Entropy-Shapley Games for Multivariate Predictive Uncertainty
Leibniz Institute for Prevention Research and Epidemiology – BIPS（莱布尼茨预防研究与流行病学研究所——BIPS）；University of Bremen（不来梅大学）；Simula Research Laboratory（西穆拉研究实验室）；Telenor Research & Innovation（挪威电信研究与创新部）；Norwegian Computing Center（挪威计算中心）
Predictive State Representations (PSRs) are powerful techniques for modelling dynamical systems, which represent a state as a vector of predictions about future observable events (tests). In PSRs, one of the fundamental problems is the learning of the PSR model of the underlying system. Recently, spectral methods have been successfully used to address this issue by treating the learning problem as the task of computing an singular value decomposition (SVD) over a submatrix of a special type of matrix called the Hankel matrix. Under the assumptions that the rows and columns of the submatrix of …
Integrated Gradients (IG), one of the most popular explainability methods available, still remains ambiguous in the selection of baseline, which may seriously impair the credibility of the explanations. This study proposes a new uniform baseline, i.e., the Maximum Entropy Baseline, which is consistent with the "uninformative" property of baselines defined in IG. In addition, we propose an improved ablating evaluation approach incorporating the new baseline, where the information conservativeness is maintained. We explain the linear transformation invariance of IG baselines from an information …
Over the past decade there has been considerable interest in spectral algorithms for learning Predictive State Representations (PSRs). Spectral algorithms have appealing theoretical guarantees; however, the resulting models do not always perform well on inference tasks in practice. One reason for this behavior is the mismatch between the intended task (accurate filtering or prediction) and the loss function being optimized by the algorithm (estimation error in model parameters). A natural idea is to improve performance by refining PSRs using an algorithm such as EM. Unfortunately it is not obv…
We present PredRNN++, an improved recurrent network for video predictive learning. In pursuit of a greater spatiotemporal modeling capability, our approach increases the transition depth between adjacent states by leveraging a novel recurrent unit, which is named Causal LSTM for re-organizing the spatial and temporal memories in a cascaded mechanism. However, there is still a dilemma in video predictive learning: increasingly deep-in-time models have been designed for capturing complex variations, while introducing more difficulties in the gradient back-propagation. To alleviate this undesirab…
