Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the information contained in some distribution of interest is its entropy. Greedily minimizing the expected entropy is therefore a standard method for choosing samples in order to gain strong beliefs about the underlying random variables. We show that this approach is prone to temporally getting stuck in local optima corresponding to wrongly biased beliefs. We suggest instead maximizing the expected cross entropy between old and new belief, which aims at challenging refutable beliefs and thereby avoids these local optima. We show that both criteria are closely related and that their difference can be traced back to the asymmetry of the Kullback-Leibler divergence. In illustrative examples as well as simulated and real-world experiments we demonstrate the advantage of cross entropy over simple entropy for practical applications.
BED-LLM: Intelligent Information Gathering with LLMs and Bayesian Experimental Design
University of Oxford（牛津大学）；Apple（苹果公司）；City University of Hong Kong（香港城市大学）；University of Somewhere（某大学）；Institute of Something（某研究所）；Company Ltd（某有限公司）
DeepMind；California Institute of Technology（加州理工学院）；Mila；Université de Montréal（蒙特利尔大学）；University of Cambridge（剑桥大学）
Policy networks are a central feature of deep reinforcement learning (RL) algorithms for continuous control, enabling the estimation and sampling of high-value actions. From the variational inference perspective on RL, policy networks, when used with entropy or KL regularization, are a form of \textit{amortized optimization}, optimizing network parameters rather than the policy distributions directly. However, \textit{direct} amortized mappings can yield suboptimal policy estimates and restricted distributions, limiting performance and exploration. Given this perspective, we consider the more …
Trust Region Policy Optimization (TRPO) is a popular and empirically successful policy search algorithm in reinforcement learning (RL). It iteratively solved the surrogate problem which restricts consecutive policies to be close to each other. TRPO is an on-policy algorithm. On-policy methods bring many benefits, like the ability to gauge each resulting policy. However, they typically discard all the knowledge about the policies which existed before. In this work, we use a replay buffer to borrow from the off-policy learning setting to TRPO. Entropy regularization is usually used to improve po…
MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）
We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We extend this notion to Renyi common entropy by minimizing the Renyi entropy of the latent variable. To efficiently compute common entropy, we propose an iterative algorithm that can be used to discover the trade-off between the entropy of the latent variable and the conditional mutual information of the observed variables. We show two applications of common ent…
Robotics Design Laboratory, University of Queensland（昆士兰大学机器人设计实验室）
Soft Actor-Critic (SAC) is one of the state-of-the-art off-policy reinforcement learning (RL) algorithms that is within the maximum entropy based RL framework. SAC is demonstrated to perform very well in a list of continous control tasks with good stability and robustness. SAC learns a stochastic Gaussian policy that can maximize a trade-off between total expected reward and the policy entropy. To update the policy, SAC minimizes the KL-Divergence between the current policy density and the soft value function density. Reparameterization trick is then used to obtain the approximate gradient of …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
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 seq…
University of Alberta（阿尔伯塔大学）；University of Oxford（牛津大学）；Technical University Delft（代尔夫特理工大学）
Information gathering in a partially observable environment can be formulated as a reinforcement learning (RL), problem where the reward depends on the agent's uncertainty. For example, the reward can be the negative entropy of the agent's belief over an unknown (or hidden) variable. Typically, the rewards of an RL agent are defined as a function of the state-action pairs and not as a function of the belief of the agent; this hinders the direct application of deep RL methods for such tasks. This paper tackles the challenge of using belief-based rewards for a deep RL agent, by offering a simple…
Fast Policy Learning for Linear Quadratic Control with Entropy Regularization
Department of Industrial Engineering & Operations Research, University of California, Berkeley（工业工程与运营管理系，加州大学伯克利分校）；Department of Mathematics, University of Oxford（数学系，牛津大学）；Department of Management Science & Engineering, Stanford University（管理科学与工程系，斯坦福大学）
Carnegie Mellon University（卡内基梅隆大学）；University of Pennsylvania（宾夕法尼亚大学）
This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding the last-iterate convergence of extragradient methods in the unconstrained setting, the theoretical underpinnings of these methods in the constrained settings, especially those using multiplicative updates, remain highly inadequate, even when the objective function is bilinear. Motivated by the algorithmic role of entropy regularization in single-agent reinfo…
Local Entropy Search over Descent Sequences for Bayesian Optimization
Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Germany（机械工程数据科学研究所，亚琛工业大学，德国）；Learning Systems and Robotics Lab, Technical University of Munich, Germany（学习系统与机器人实验室，慕尼黑技术大学，德国）
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we argue that for classiffication tasks, mutual information is a more suitable information theoretic measure to be optimized. We show how the principle of minimum mutual information generalizes that of maximum entropy, and provides a comprehensive framework for building discriminative classiffiers. A game theoretic interpretation of our approach is then given, and…
University of Wisconsin Madison（威斯康星大学麦迪逊分校）；Brown University（布朗大学）；University of Chicago（芝加哥大学）
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimization, based on the iterative shift of a probability density and the calculation of a best Gaussian approximation in Kullback-Leibler divergence. Under this unified light, the optimization schemes for local entropy and heat regularized loss differ only over which argument of the Kull…
Imperial College London（帝国理工学院）；Data Science Institute, Imperial College London（帝国理工学院数据科学研究所）
Denoising autoencoders (DAEs) are powerful deep learning models used for feature extraction, data generation and network pre-training. DAEs consist of an encoder and decoder which may be trained simultaneously to minimise a loss (function) between an input and the reconstruction of a corrupted version of the input. There are two common loss functions used for training autoencoders, these include the mean-squared error (MSE) and the binary cross-entropy (BCE). When training autoencoders on image data a natural choice of loss function is BCE, since pixel values may be normalised to take values i…
Anyvision Research Team（Anyvision研究团队）；Queen’s University Belfast（贝尔法斯特女王大学）
Loss functions play a crucial role in deep metric learning thus a variety of them have been proposed. Some supervise the learning process by pairwise or tripletwise similarity constraints while others take advantage of structured similarity information among multiple data points. In this work, we approach deep metric learning from a novel perspective. We propose instance cross entropy (ICE) which measures the difference between an estimated instance-level matching distribution and its ground-truth one. ICE has three main appealing properties. Firstly, similar to categorical cross entropy (CCE)…
