arXiv research

The paper studies horofunction compactifications of symmetric cones under Finsler distances.

New bounds found for complexity of spun knots.

Sharp bounds for Kirby-Thompson invariants of knotted surfaces computed.

New invariant measures knotted surfaces in 4D, revealing unknottedness.

The distance from the origin in the word metric for generalizations F(p) of Thompson's group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of F(p). This interpretation of the metric is used to prove that every F(p) admits a quasi-isometric embedding into ever…

This paper states a formula for the difference of the Holmes-Thompson volumes of two simple Finsler manifolds of arbitrary dimension, in terms of the boundary distances and their derivatives. An application is a preconditioned filling minimality result.

We show that the volume of a simple Riemannian metric on $D^n$ is locally monotone with respect to its boundary distance function. Namely if $g$ is a simple metric on $D^n$ and $g'$ is sufficiently close to $g$ and induces boundary distances greater or equal to those of $g$, then $vol(D^n,g')\ge vol(D^n,g)$. Furthermor…

We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a combinatorial version of a proof by Hass, Thompson and Thurston of a similar theorem, bu…

The paper sets lower bounds for a Kirby-Thompson invariant of 4-manifolds.

New algorithm finds k-centers from noisy distance estimates.

Develops a combinatorial semi-bandit method for electric vehicle charging station selection.

A new approach for efficient batch multiobjective optimization using Thompson sampling.

Positive Thompson links are arborescent tangles.

Positive Thompson links are proven for oriented subgroup elements.

Thompson sampling provides a solution to bandit problems in which new observations are allocated to arms with the posterior probability that an arm is optimal. While sometimes easy to implement and asymptotically optimal, Thompson sampling can be computationally demanding in large scale bandit problems, and its perform…

Jones constructs knots from Thompson group elements.

New method counts link components from Thompson group elements.

Extends Jones' construction to Thompson's group F and link homology.

Optimizes Thompson sampling policies using policy gradient methods.

New Thompson sampling uses local uncertainty for better decision making.

This paper proves a conjecture about trisections with a specific length.

MOTS improves Thompson sampling to match minimax bounds for bandit problems.

New method targets vaccines for new variants using Thompson sampling.

Thompson sampling has impressive empirical performance for many multi-armed bandit problems. But current algorithms for Thompson sampling only work for the case of conjugate priors since these algorithms require to infer the posterior, which is often computationally intractable when the prior is not conjugate. In this …

Improved Thompson Sampling reduces regret in contextual bandits and reinforcement learning.

New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.

Brin-Thompson groups have new properties for n>=2.

New $p$-colorable subgroup derived from Thompson's group.

New family of braided Thompson groups introduced using recursive braids.

Extends Thompson sampling for RL with fewer episodes.

Thompson sampling, a Bayesian method for balancing exploration and exploitation in bandit problems, has theoretical guarantees and exhibits strong empirical performance in many domains. Traditional Thompson sampling, however, assumes perfect compliance, where an agent's chosen action is treated as the implemented actio…

New virtual version of Thompson's group created to handle virtual knots.

Study of quasimorphisms and bounded cohomology in braided Thompson groups.

Improved Thompson Sampling algorithms for bandits with tighter regret bounds.

Thompson sampling used for linear bandits with normal-gamma priors.

We consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson's groups by infinite (spherical) braid groups. We will outline the main features of these groups and some applications to …

A new thompson sampling method controls for time-varying effects.

Improved Thompson Sampling for smoother functions with noise.

New method associates annular links to elements of Thompson's group T.

Thompson Sampling, one of the oldest heuristics for solving multi-armed bandits, has recently been shown to demonstrate state-of-the-art performance. The empirical success has led to great interests in theoretical understanding of this heuristic. In this paper, we approach this problem in a way very different from exis…

Paper improves Thompson Sampling for linear contextual bandits.

Improved Thompson sampling for bandits with Langevin algorithms.

Half grid diagrams prove every link can be represented by a special type of grid diagram.

New methods use Conway tangles to generate knots and links.

Improved statistical inference for adaptive Thompson Sampling.

We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson groups F, V, Vbr and Fbr arise from this procedure using, respectively, the systems of trivial groups, symmetric groups, braid groups and pur…

This paper explores links from Thompson's group conjugacy classes.

This paper applies Thompson Sampling to asymmetric $\alpha$-stable bandits for financial and wireless data.