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…
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48 results for “Thompson metric”
A new geometric method for clustering SPD data improves upon Euclidean and Riemannian approaches.
problem Skewed interpretations of SPD data in Euclidean analysis and computational inefficiency of Riemannian methods.
method Proposes a geometric method based on the Thompson metric for unsupervised clustering of SPD data.
result Demonstrates improved clustering results using inductive midrange centroid computation.
Scharlemann and Thompson define a numerical complexity for a 3-manifold using handle decompositions of the manifold. We show that for compact hyperbolic 3-manifolds this is linearly related to a definition of metric complexity in terms of the areas of level sets of Morse functions.
We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this r…
The paper tightens the regret rate for linear bandit problems.
problem Bayesian regret in linear bandit problems.
method Information-theoretic framework and chaining argument.
result Established a new bound with a tight rate of .
The study connects polygon areas and projective structures in 3D space.
problem Relating polygon areas and projective structures in 3D space.
method Investigates positive tuples of complete flags in R^3 and their associated polygons in RP^2.
result Establishes a relationship between Holmes-Thompson area and projective structures.
The paper proposes extensions of the usual notions of Finslerian volume to time orientable Finsler spacetime manifolds. The basic idea is to replace, in the classical Busemann-Hausdorff and Holmes-Thompson definitions, integration on the indicatrices of the given metric (which are, in Lorentzian signature, non-compact,…
The paper sets lower bounds for a Kirby-Thompson invariant of 4-manifolds.
problem Determining the Kirby-Thompson invariant of specific 4-manifolds.
method Using trisections, the paper establishes lower bounds and calculates the invariant for specific examples.
result The paper calculates the Kirby-Thompson invariant of the spin of and shows the existence of 4-manifolds with arbitrarily large invariants.
Positive Thompson links are arborescent tangles.
problem Understanding the structure of Thompson group elements.
method Analyzing closures of bipartite arborescent tangles.
result Positive Thompson links correspond to arborescent tangles.
Positive Thompson links are proven for oriented subgroup elements.
problem Proving properties of Thompson links with positive elements.
method Analyzing elements of the oriented subgroup of the Thompson group.
result Positive oriented Thompson links are established.
The minimal area of Finsler disks with minimizing geodesics is at least 6/π r^2.
problem Finding the minimal area of Finsler disks with minimizing geodesics.
method Discretizing the Finsler metric using random geodesics and applying integral geometry formulas.
result The Holmes--Thompson area of Finsler disks with minimizing geodesics is at least 6/π r^2, with examples showing the inequality is sharp.
New Finsler metric on sphere disproves systolic ratio conjecture.
problem Proving the maximal systolic ratio on 2-sphere.
method Inspired by Cossarini-Sabourau, constructs a Finsler metric.
result Systolic ratio of new Finsler metric is .
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.
problem No specific problem stated; focuses on constructions.
method Constructions of knots from Thompson group elements.
result Introduced two types of knots: oriented and unoriented.
New method counts link components from Thompson group elements.
problem Counting connected components of positive Thompson links.
method Defining Thompson permutations from Thompson group elements.
result Number of orbits equals number of link components.
Extends Jones' construction to Thompson's group F and link homology.
problem Link homology and Thompson's group F.
method Asymptotic construction of -tangles in Thompson's group F.
result Asymptotically faithful association of -tangles with elements of Thompson's group F.
We prove optimal systolic inequalities on Finsler Mobius bands relating the systole and the height of the Mobius band to its Holmes-Thompson volume. We also establish an optimal systolic in- equality for Finsler Klein bottles of revolution, which we conjecture to hold true for arbitrary Finsler metrics. Extremal metric…
Optimizes Thompson sampling policies using policy gradient methods.
problem Improving Thompson sampling in bandit problems.
method Applies policy gradient algorithms to optimize Thompson sampling policies.
result Direct policy search on Thompson sampling improves performance.
This paper proves a conjecture about trisections with a specific length.
problem Proving a conjecture about trisections with a specific length.
method Examining trisections with Kirby-Thompson length 2 and proving the conjecture.
result Proves the conjecture about length 2 trisection being a 4-manifold with length 0.
MOTS improves Thompson sampling to match minimax bounds for bandit problems.
problem Achieving optimal regret bounds for Thompson sampling in multi-armed bandit problems.
method Proposes MOTS, a variant of Thompson sampling that clips arm sampling.
result Proves MOTS achieves minimax optimal regret bounds .
New method targets vaccines for new variants using Thompson sampling.
problem Deciding how to prioritize vaccines for new variants with delayed feedback.
method Partial likelihood Thompson sampling, updating beliefs with partial likelihood.
result Method effectively prioritizes vaccines based on real-world data.
New bounds found for complexity of spun knots.
problem Measuring complexity of spun knots.
method Using bridge trisections and distances in the pants complex.
result Bound the Kirby-Thompson invariant 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.
problem Thompson Sampling's exploration is insufficient in some contexts.
method Developed Feel-Good Thompson Sampling to address exploration issues.
result Feel-Good Thompson Sampling reduces regret compared to standard Thompson Sampling.
New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.
problem Limited feedback in sequential learning problems.
method Developed a novel Thompson-sampling-based algorithm to sample from the posterior distribution exactly.
result Achieved logarithmic regret bound of O(log T) for a linearized variant of the problem.
Brin-Thompson groups have new properties for n>=2.
problem Characterize subgroups of Brin-Thompson groups.
method Analyzing torsion and subgroup structure.
result Brin-Thompson groups for contain continuum many copies of .
New -colorable subgroup derived from Thompson's group.
problem Constructing -colorable knots and links from Thompson's group elements.
method Defining and proving isomorphism of -colorable subgroup.
result The -colorable subgroup is isomorphic to a Brown--Thompson group.
New family of braided Thompson groups introduced using recursive braids.
problem Dehornoy-Brin braided Thompson group generalization.
method Using recursive braids and strand diagrams to define new groups.
result New groups are finitely generated if is finitely generated.
Extends Thompson sampling for RL with fewer episodes.
problem Limited episodes in RL settings.
method Batch Bayesian optimization over episodes to learn action bias terms.
result Significantly outperforms standard Thompson sampling.
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…
Virtual Thompson's groupmath.GT
New virtual version of Thompson's group created to handle virtual knots.
problem Creating a mathematical framework for virtual knots.
method Defining a virtual version of Thompson's group and proving its properties.
result Any virtual link can be constructed from an element of the new virtual Thompson's group.
Study of quasimorphisms and bounded cohomology in braided Thompson groups.
problem Investigate quasimorphisms and bounded cohomology in braided versions of Thompson groups.
method Analyze quasimorphisms and bounded cohomology of various braided Thompson groups.
result Found infinite-dimensional spaces of quasimorphisms in some braided Thompson groups and trivial second bounded cohomology in others.
Thompson sampling used for linear bandits with normal-gamma priors.
problem Optimizing decisions in uncertain environments with linear dependencies and unknown parameters.
method Bayesian Thompson sampling with multivariate normal-gamma priors.
result Derivation of a Bayesian regret bound for the approach.
Improved Thompson Sampling algorithms for bandits with tighter regret bounds.
problem Efficient and adaptive algorithms for stochastic bandits with bounded rewards.
method Proposed two parameterized Thompson Sampling-based algorithms: TS-MA-α and TS-TD-α.
result Achieved O(Kln^(α+1)(T)/Δ) regret bound, improving scalability and resource allocation.
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.
problem Dynamic experiments in online services with time-varying effects.
method Odds-ratio Thompson Sampling
result The proposed method works robust to time-varying effects.
This paper improves Thompson Sampling for complex decision-making problems.
problem Learning in infinite-horizon discounted decision processes with unknown parameters.
method Developed a general canonical probability space and new metrics for analyzing adaptive learning algorithms.
result Thompson Sampling achieves complete learning in complex decision-making problems.
Improved Thompson Sampling for smoother functions with noise.
problem Applying Thompson Sampling to continuum armed bandits with weak conditions.
method Analysis of eluder dimension for function classes with smooth derivatives.
result New bounds on eluder dimension for classes of functions with Lipschitz derivatives.
New method associates annular links to elements of Thompson's group T.
problem Associating annular links to elements of Thompson's group T.
method Edge-signed graphs embedded in annuli and unitary representations of T.
result Tait graphs of annular links can be constructed from elements of 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.
problem Empirical Thompson Sampling does not achieve optimal regret bounds.
method Develops a novel estimator with adaptive data augmentation and coupling.
result Achieves nearly minimax optimal performance.
Improved Thompson sampling for bandits with Langevin algorithms.
problem Thompson sampling's computational inefficiency in generating posterior samples.
method Developed Langevin algorithms for approximate sampling with posterior concentration guarantees.
result Logarithmic regret with constant computational complexity.
Half grid diagrams prove every link can be represented by a special type of grid diagram.
problem Representing links using grid diagrams and related invariants.
method Defining half grid diagrams and constructing canonical pairs, proving equivalence to Jones' construction, relating to classical link invariants.
result Established a new method to relate the oriented Thompson index to classical link invariants and provided bounds for knot invariants.
The paper proposes a notion of volume element for Finsler spaces with metrics of Lorentzian signature, equipped with a time orientation. This notion is based on a slight modification of the idea of Holmes-Thompson volume element working for positive definite Finsler metrics and can be used in field-theoretical applicat…
New methods use Conway tangles to generate knots and links.
problem Constructing knots and links using Thompson's group elements.
method Using Conway rational tangles to find Thompson group elements.
result Methods to construct any product or concatenation of simple tangles.
Thompson sampling is an efficient algorithm for sequential decision making, which exploits the posterior uncertainty to address the exploration-exploitation dilemma. There has been significant recent interest in integrating Bayesian neural networks into Thompson sampling. Most of these methods rely on global variable u…
Improved statistical inference for adaptive Thompson Sampling.
problem Statistical inference challenges in Thompson Sampling.
method Inflating posterior variance in Thompson Sampling.
result Asymptotically normal estimates of arm means with logarithmic regret increase.
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…