State entropy regularization improves robustness in reinforcement learning, especially under structured perturbations.
problem Structured and spatially correlated perturbations in reinforcement learning.
method State entropy regularization, compared to policy entropy.
result State entropy regularization provides better robustness to structured and spatially correlated perturbations.
This work improves policy optimization by maximizing entropy of state distribution, leading to better exploration.
problem Lack of exploration in state space when maximizing policy entropy.
method Proposes maximizing the entropy of a lower bound approximation to the state weighting distribution, based on latent space representation.
result Entropy regularization based on marginal state distribution achieves superior state space coverage and better performance in various domains.
Paper proposes a policy-search algorithm to learn entropy-maximizing exploration policies in reward-free environments.
problem Reward-free learning in high-dimensional, continuous-control domains.
method Maximum Entropy POLicy optimization (MEPOL) algorithm that maximizes a non-parametric state entropy estimate.
result MEPOL learns a maximum-entropy exploration policy that facilitates learning various reward-based tasks.
The study bounds entanglement entropy for coherent states on Kähler manifolds.
problem Bounding entanglement entropy for coherent states on Kähler manifolds.
method Geometric quantization and Hilbert spaces of Kähler manifolds.
result Positive lower bounds for entanglement entropy are provided asymptotically.
The paper introduces a new intrinsic reward method for exploration in reinforcement learning.
problem Improving exploration in reinforcement learning agents.
method Intrinsic rewards proportional to the entropy of future state-action features.
result The new objective leads to improved visitation of features within individual trajectories.
A new IRL model recovers reward and state structure from expert demonstrations.
problem Limitation of classical maximum entropy model in capturing state structure.
method Generalized maximum causal entropy for IRL models.
result Empirically outperforms classical models in recovering reward and state structure.
A neural network method estimates entropy production from system trajectories.
problem Estimating entropy production from system trajectories without detailed dynamics.
method Developed a neural estimator (NEEP) for entropy production (EP).
result NEEP rigorously proves to provide stochastic EP by optimizing an objective function.
New RL approach uses future state and action visitation measures for better exploration.
problem Improving exploration in reinforcement learning.
method Intrinsic reward based on future state and action visitation measures, using contraction operators.
result Policies achieve good state-action space coverage and high performance.
Study on quantum state entanglement using Kaehler manifolds.
problem Quantum state entanglement on Kaehler manifolds.
method Semiclassical asymptotics and pure states on spheres.
result Entropy analysis of quantum states on spheres.
New method uses entropy to improve policy gradient exploration.
problem Limited exploration in policy gradient methods.
method Entropy regularization with discounted future state distribution.
result Proves convergence to locally optimal policy.
Proposes integrating global and local entropy for more reliable LLMs.
problem Uncertainty in large language models (LLMs) leads to unreliable predictions.
method Measures global uncertainty from hidden-state matrices and local uncertainty from tokens, combining them via a multiplicative gate.
result Global-Local Uncertainty (GLU) outperforms unsupervised baselines across multiple models and benchmarks.
Study Transformer layers under cross-entropy training using mean field control.
problem Understanding the behavior of Transformer layers in cross-entropy training.
method Continuous-depth mean field control analysis, treating depth as time and layer parameters as controls.
result Derivation of a Pontryagin condition for the limiting population problem, involving the softmax residual.
PEOC uses policy entropy to detect untrained states in RL.
problem Detecting untrained states in reinforcement learning for safety.
method Policy entropy based one-class classifier.
result PEOC is highly competitive and reliable.
Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the…
Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.
problem Estimating relaxation times in financial market dynamics.
method Developing a method using EGF for maximizing Tsallis entropy.
result Longer relaxation times for nonextensive systems compared to Shannon entropy.
We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the conve…
Paper proves Jeffrey's update rule minimizes relative entropy.
problem Improving Bayesian learning algorithms.
method More concise proof of Jeffrey's update rule.
result Jeffrey's update rule reduces relative entropy.
This paper improves reinforcement learning policies in a scalable way.
problem Ensuring monotonic policy improvement in entropy-regularized RL.
method Derives an entropy-aware lower bound and proposes a novel RL algorithm.
result Demonstrates effectiveness in continuous-state tasks using a linear function approximator.
This study proposes hidden state curiosity to enhance RL models' resilience against noise.
problem Curiosity traps in RL models distract agents from discovering novel experiences.
method Proposed hidden state curiosity based on the Free Energy Principle to reward agents for KL divergence between predictive priors and posteriors.
result Agents with hidden state curiosity are more resilient against curiosity traps compared to those with prediction error curiosity.
Tree-AMP simplifies inference in complex tree-structured models.
problem Inference in high-dimensional tree-structured models.
method Approximate Message Passing algorithms for various machine learning tasks.
result Theoretical performance predictions and automated entropy estimation.
Enhances RL by controlling policy stochasticity through trajectory entropy constraints.
problem Non-stationary Q-value estimation and short-sighted entropy tuning in maximum entropy RL.
method Proposes TECRL framework with separate Q-functions for reward and entropy, enforcing a trajectory entropy constraint.
result DSAC-E algorithm achieves higher returns and better stability on OpenAI Gym benchmarks.
In 1870s, L. Boltzmann proved the famous H-theorem for the Boltzmann equation in the kinetic theory of gas and gave the statistical interpretation of the thermodynamic entropy. In 2002, G. Perelman introduced the notion of W-entropy and proved the W-entropy formula for the Ricci flow. This plays a crucial role in…
In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…
We study a new ensemble of random correlation matrices related to multivariate Student (or more generally elliptic) random variables. We establish the exact density of states of empirical correlation matrices that generalizes the Marcenko-Pastur result. The comparison between the theoretical density of states in the St…
We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to accommodate convex regularization functions. Our key result is showing that using the …
This thesis applies entropy as a model independent measure to address three research questions concerning financial time series. In the first study we apply transfer entropy to drawdowns and drawups in foreign exchange rates, to study their correlation and cross correlation. When applied to daily and hourly EUR/USD and…
JES optimizes expensive functions by considering joint entropy over input and output spaces.
problem Optimizing expensive functions with limited evaluations.
method Joint Entropy Search (JES) considers joint entropy over input and output spaces.
result JES outperforms other information-theoretic methods in Bayesian optimization.
In recent years, deep reinforcement learning has been shown to be adept at solving sequential decision processes with high-dimensional state spaces such as in the Atari games. Many reinforcement learning problems, however, involve high-dimensional discrete action spaces as well as high-dimensional state spaces. This pa…
Proposes MEDM to balance entropy minimization and diversity maximization for better domain adaptation.
problem Trivial solutions in entropy minimization for unsupervised domain adaptation.
method Introduces diversity maximization to balance with entropy minimization, controlled by deep embedded validation.
result MEDM outperforms state-of-the-art methods on four domain adaptation datasets.
A new algorithm learns diverse policies in reinforcement learning.
problem Learning diverse behaviors in reinforcement learning.
method Proposes Maximum Entropy Diverse Exploration (MEDE) algorithm.
result The set of policies learned by MEDE capture the same modalities as the optimal maximum entropy policy.
Entropy-regularized NPG converges linearly with linear function approximation.
problem Analyzing convergence of entropy-regularized NPG with function approximation.
method Established finite-time convergence analyses with entropy regularization and linear function approximation.
result Entropy-regularized NPG achieves linear convergence up to a function approximation error.
Optimal control in latent factor models uses Tsallis entropy for exploration.
problem Optimal control in models with latent factors.
method Reward exploration with Tsallis entropy and derive q-Gaussian distribution over states. result Optimal policy derived in a model-agnostic setting.
Study shows depth improves generalization in deep learning models.
problem Understanding why and when depth improves generalization in deep learning.
method Implementation-agnostic state-transition model to analyze depth and generalization.
result Identifies geometric and semigroup mechanisms that keep entropy contribution saturated or polynomial, clarifying depth's statistical advantage.
Many policy gradient methods are variants of Actor-Critic (AC), where a value function (critic) is learned to facilitate updating the parameterized policy (actor). The update to the actor involves a log-likelihood update weighted by the action-values, with the addition of entropy regularization for soft variants. In th…
The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{po…
Differentiable PF via entropy-regularized OT for better inference.
problem Non-differentiability of traditional PF resampling methods.
method Entropy-regularized optimal transport for differentiable resampling.
result Convergent differentiable PF method with improved gradient estimates.
A streamlined DRL algorithm improves sample efficiency without entropy maximization.
problem Improving sample efficiency in off-policy DRL algorithms.
method Output normalization and non-uniform sampling.
result Proposed algorithm matches SAC's performance without entropy maximization and improves sample efficiency.
AR-DAE approximates entropy gradient for machine learning models.
problem Intractable computation of entropy gradient for continuous distributions.
method Amortized residual denoising autoencoder (AR-DAE) to approximate entropy gradient.
result AR-DAE provides an unbiased gradient approximation for entropy.
Paper introduces a new measure combining entropy and Gini index.
problem Quantifying complexity in socio- and econo-physics.
method Generalizes entropy using Gini index and Lorenz curve transformation.
result Supports quantifying complexity in socio- and econo-physics.
Coupled entropy corrects flaws in Tsallis entropy for complex systems.
problem Misinterpretation of generalized temperature and entropy.
method Derived from generalized Pareto and Student's t distributions.
result Provides balanced measure of uncertainty for complex systems.
The financial market entropy is modeled using open quantum systems.
problem Understanding entropy in financial market dynamics.
method Using Open Quantum Systems to model entropy gain in financial markets.
result Interesting non-classical results generated by relaxing assumptions.
Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its returns. We achieve this by using an objective function that relies on the exponential…
We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but makes the assumption that the unobserved exogenous variable has small entropy in t…
The article presents a new entropy model for assessing stock market interest.
problem Assessing investor interest and market sentiment in exchange-traded securities.
method Intrinsic entropy model using actual trading data, without exogenous factors.
result Empirical evidence supports the model's ability to predict trading activity.
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entro…
New algorithms reduce complexity for learning in MDPs with entropy regularization.
problem Efficient learning for MDPs with large or continuous state and action spaces.
method Multilevel Monte Carlo (MLMC) algorithms integrating fixed-point iteration and stochastic approximation of the Bellman operator.
result MLMC with unbiased approximation of the Bellman operator achieves polynomial sample complexity.
Trust-region methods have yielded state-of-the-art results in policy search. A common approach is to use KL-divergence to bound the region of trust resulting in a natural gradient policy update. We show that the natural gradient and trust region optimization are equivalent if we use the natural parameterization of a st…
We present a new method of generating mixture models for data with categorical attributes. The keys to this approach are an entropy-based density metric in categorical space and annealing of high-entropy/low-density components from an initial state with many components. Pruning of low-density components using the entro…