arXiv research

New proof for sphere recognition algorithm.

Earlier work with Robert Gompf and Abigail Thompson classified, via a natural slope indexed by the rationals, all two-component links which contain the square knot and from which $(S^1 \times S^2) \# (S^1 \times S^2)$ can be obtained by surgery. It was argued that a certain family $L_n$ of such links probably contradic…

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

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.

New bounds found for complexity of spun knots.

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.

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

Improved Thompson Sampling for high-dimensional sparse bandits.

Paper proves almost all stabilizer subgroups of Thompson's group satisfy Alexander's theorem.

The group of $\mathcal C^1$-diffeomorphisms of any sparse Cantor subset of a manifold is countable and discrete (possibly trivial). Thompson's groups come out of this construction when we consider central ternary Cantor subsets of an interval. Brin's higher dimensional generalizations $nV$ of Thompson's group $V$ arise…

TS-Insight visualizes Thompson Sampling for better debugging and trust.

Model shows screening for infectious disease is hard but Thompson sampling works well.

We review recent developments in the theory of Thompson group representations related to knot theory.

ERTS uses Thompson sampling for Gaussian entropic risk bandits, achieving regret bounds.