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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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4489133177 · May 202619922001200920172026
48 results for Thompson geometry

New scalable geometric framework for SPD matrices.

problem Costly spectral computations in SPD matrix analysis.
method Efficient computation of extreme generalized eigenvalues through Hilbert and Thompson geometries of the semidefinite cone.
result Existence and uniqueness of a novel iterative mean of SPD matrices.

Geometric framework for SPD matrices preserving subspace structures.

problem Processing SPD-valued data with preserved subspace structures.
method Thompson geometry of the semidefinite cone, extreme generalized eigenvalues, geodesic space structure.
result Novel inductive mean of SPD matrices based on Thompson geometry.

New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.

problem Defining a symplectic invariant for Weinstein domains.
method Contact cut graph, Lefschetz fibrations, multisections with divides.
result Definition of Weinstein L\mathcal{L}-invariant and its relation to Kirby-Thompson's invariant.

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 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.

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 L(2,1)L(2,1) and shows the existence of 4-manifolds with arbitrarily large invariants.

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…

2014-10-15abs ↗pdf ↗

We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a…

2014-06-29abs ↗pdf ↗

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.

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…

2018-12-03abs ↗pdf ↗

New technique tracks geometric properties to correct base algorithms' poor performance.

problem Discrepancy between empirical performance and theoretical regret bounds in linear bandits.
method Data-driven technique that incorporates geometric information to formulate frequentist regret bound.
result Course-corrected algorithms achieve minimax optimal regret of ildeO(dT) ilde{\mathcal{O}}(d\sqrt{T}).

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.

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 …

2011-05-03abs ↗pdf ↗

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…

2013-10-27abs ↗pdf ↗

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.

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…

2019-10-30abs ↗pdf ↗

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…

2014-05-21abs ↗pdf ↗

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

problem Understanding the relationship between Thompson's group conjugacy classes and links.
method Using Jones's construction to link elements of FF to unoriented links.
result Found sequences of elements from distinct conjugacy classes yielding specific links.