Related papers: Tsallis Entropy Regularization for Linearly Solvab…
It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.
We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion…
The quantization problem aims to find the best possible approximation of probability measures on ${\mathbb{R}}^d$ using finite, discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation.…
This paper extends our previous study on an explicit saturated control for a quadcopter, which ensures both constraint satisfaction and stability thanks to the linear representation of the system in the flat output space. The novelty here…
We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, R\'enyi, generalized R\'enyi, Tsallis, Sharma-Mittal, and modified Shannon entropy,…
Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid…
Reinforcement Learning (RL) has shown great potential in complex control tasks, particularly when combined with deep neural networks within the Actor-Critic (AC) framework. However, in practical applications, balancing exploration, learning…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
Nonextensive entropies are divided into three classes, each of which is characterized by Shannon additivity and pseudoadditivity. One of the three classes has properties of both additivities. The remaining classes have only one property of…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
Maximum entropy has become a mainstream off-policy reinforcement learning (RL) framework for balancing exploitation and exploration. However, two bottlenecks still limit further performance improvement: (1) non-stationary Q-value estimation…
We study minimization of a parametric family of relative entropies, termed relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}(P,Q)$). These arise as redundancies under mismatched compression when cumulants of compressed lengths are…
The quantum relative Renyi entropy of two density matrices was recently extended when the two do not commute, from which a conditional entropy is identified. This is here extended to the corresponding Tsallis relative entropy and to its…
Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic…
The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On…
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
Reinforcement learning (RL) has been successfully used to solve many continuous control tasks. Despite its impressive results however, fundamental questions regarding the sample complexity of RL on continuous problems remain open. We study…
Compressed Counting (CC)} was recently proposed for approximating the $\alpha$th frequency moments of data streams, for $0<\alpha \leq 2$. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on…
Many potential applications of reinforcement learning (RL) require guarantees that the agent will perform well in the face of disturbances to the dynamics or reward function. In this paper, we prove theoretically that maximum entropy…
The cyclic Lotka-Volterra model in a $D$-dimensional regular lattice is considered. Its ``nucleus growth'' mode is analyzed under the scope of Tsallis' entropies $S_q=(1-\sum_i p_i^q)/(q-1)$, $q\in \mathbb{R}$. It is shown both numerically…