Related papers: Generalized Maximum Entropy Differential Dynamic P…

In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…

We derive a scaling property from a fundamental nonlinear differential equation whose solution is the so-called q-exponential function. A scaling property has been believed to be given by a power function only, but actually more general…

We study the trajectory optimization problem under chance constraints for continuous-time stochastic systems. To address chance constraints imposed on the entire stochastic trajectory, we propose a framework based on the set erosion…

We generalize the completely monotone conjecture ([CG15]) from Shannon entropy to the Tsallis entropy up for orders up to at least four. To this end, we employ the algorithm ([J\"un16, JM06a]) which employs the technique of systematic…

Following the work on Shannon entropy together with the principle of maximum entropy, Luo & Singh (J. Hydrol. Eng., 2011, 16(4): 303-315) and Singh & Luo (J. Hydrol. Eng., 2011, 16(9): 725-735) explored the concept of non-extensive Tsallis…

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy…

Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…

Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the…

We show that the max entropy algorithm can be derandomized (with respect to a particular objective function) to give a deterministic $3/2-\epsilon$ approximation algorithm for metric TSP for some $\epsilon > 10^{-36}$. To obtain our result,…

In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in…

Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…

Optimizing 3D k-space sampling trajectories for efficient MRI is important yet challenging. This work proposes a generalized framework for optimizing 3D non-Cartesian sampling patterns via data-driven optimization. We built a differentiable…

Modern statistical estimation is often performed in a distributed setting where each sample belongs to a single user who shares their data with a central server. Users are typically concerned with preserving the privacy of their samples,…

In this paper, we consider the problem of estimating Tsallis entropy from a given data set. We propose four different estimators for Tsallis entropy measure based on higher-order sample spacings, and then discuss estimation of Tsallis…

Sampling-based motion planning algorithms are widely used in robotics because they are very effective in high-dimensional spaces. However, the success rate and quality of the solutions are determined by an adequate selection of their…

We present a fairly general framework for reducing $(\varepsilon, \delta)$ differentially private (DP) statistical estimation to its non-private counterpart. As the main application of this framework, we give a polynomial time and…

This paper studies the continuous-time q-learning (the continuous time counterpart of Q-learing) for Markov switching system under Tsallis entropy regularization. We address the difficulty in traditional RL algorithms where the Tsallis…

Learning from Demonstration (LfD) has emerged as a crucial method for robots to acquire new skills. However, when given suboptimal task trajectory demonstrations with shape characteristics reflecting human preferences but subpar dynamic…

Generative flow networks (GFlowNets) are amortized variational inference algorithms that treat sampling from a distribution over compositional objects as a sequential decision-making problem with a learnable action policy. Unlike other…