Related papers: A Lower Bound for the Max Entropy Algorithm for TS…
The theory of reinforcement learning currently suffers from a mismatch between its empirical performance and the theoretical characterization of its performance, with consequences for, e.g., the understanding of sample efficiency, safety,…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
For some $\epsilon > 10^{-36}$ we give a randomized $3/2-\epsilon$ approximation algorithm for metric TSP.
Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved…
In the Shortest-Superstring problem, we are given a set of strings S and want to find a string that contains all strings in S as substrings and has minimum length. This is a classical problem in approximation and the best known…
We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
We present an algorithm based on posterior sampling (aka Thompson sampling) that achieves near-optimal worst-case regret bounds when the underlying Markov Decision Process (MDP) is communicating with a finite, though unknown, diameter. Our…
We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…
Determining the precise integrality gap for the subtour LP relaxation of the traveling salesman problem is a significant open question, with little progress made in thirty years in the general case of symmetric costs that obey triangle…
Among various variants of the traveling salesman problem, the s-t-path graph TSP has the special feature that we know the exact integrality ratio, 3/2, and an approximation algorithm matching this ratio. In this paper, we go below this…
We argue that Non-sequential Recursive Pair Substitution (NSRPS) as suggested by Jim\'enez-Monta\~no and Ebeling can indeed be used as a basis for an optimal data compression algorithm. In particular, we prove for Markov sequences that…
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra…
Post-processing of the raw bits produced by a true random number generator (TRNG) is always necessary when the entropy per bit is insufficient for security applications. In this paper, we derive a tight bound on the output min-entropy of…
We give a characterization of Maximum Entropy/Minimum Relative Entropy inference by providing two `strong entropy concentration' theorems. These theorems unify and generalize Jaynes' `concentration phenomenon' and Van Campenhout and Cover's…
Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…
The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction…
We consider the well-known max-(relative) entropy problem $\Theta$(y) = infQ$\ll$P DKL(Q P ) with Kullback-Leibler divergence on a domain $\Omega$ $\subset$ R d , and with ''moment'' constraints h dQ = y, y $\in$ R m . We show that when m…