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arXiv research

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.

168,742 papers · 148 categories

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59118176235 · Jun 202019922001200920172026
48 results for logarithmic steps

New algorithms achieve logarithmic regret in learning linear quadratic control systems.

problem Learning in Linear Quadratic Control systems with unknown parameters.
method Efficient algorithms for two scenarios: unknown AA or BB with certain conditions.
result Regret scales logarithmically with the number of steps, not square root.

Honest traders can outperform insiders in a Black-Scholes market with positive probability.

problem Comparing the performance of honest and insider traders in a financial market.
method Using anticipating stochastic calculus and forward integral analysis of the Doléans-Dade exponential process.
result The honest trader can achieve higher logarithmic utility and wealth than the insider with positive probability.

AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.

problem Adaptive control in partially observable linear dynamical systems.
method AdaptOn algorithm that estimates system dynamics through online learning and gradient descent.
result AdaptOn achieves a logarithmic regret bound of polylog(T) after T steps.

Paper analyzes and improves KL-regularized RL for LLMs with logarithmic regret.

problem Improving efficiency of RL fine-tuning for large language models.
method Optimism-based KL-regularized online contextual bandit algorithm with novel regret analysis.
result Achieves an O(ηlog(NRT)dR)\mathcal{O}\big(η\log (N_{\mathcal R} T)\cdot d_{\mathcal R}\big) logarithmic regret bound.

A new subdivision scheme for Heisenberg group values with central smoothness loss.

problem Regularity of limit curves in Heisenberg group-valued subdivision schemes.
method Interpolatory subdivision scheme with central correction based on group law.
result Central part of limit curve converges to a continuous limit with logarithmic modulus of continuity.

Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.

problem Efficiently solving ordinary differential equations (ODEs) with reduced computational cost.
method Formulated a parallel-in-time probabilistic numerical ODE solver using time-parallel formulation of iterated extended Kalman smoothers.
result Reduces span cost from linear to logarithmic in the number of time steps.

Develops a parameter-free SGD algorithm with optimal convergence rate.

problem Optimizing parameters in stochastic convex optimization.
method A novel parameter-free algorithm for SGD with high-probability guarantees and adaptive properties.
result Achieves optimal convergence rate with only a double-logarithmic factor increase compared to known-parameter settings.

Polyak step size GD reaches final radius of convergence after log iterations.

problem Statistical and computational complexities of Polyak step size GD.
method Generalized smoothness and Lojasiewicz conditions, stability of gradients.
result Polyak step size GD reaches final statistical radius of convergence after logarithmic number of iterations.

Algorithm learns expert weights to minimize regret in adversarial setting.

problem Learning to aggregate expert forecasts with no-regret guarantee in adversarial conditions.
method Online mirror descent algorithm for logarithmic pooling of expert forecasts.
result Achieves O(TlogT)O(\sqrt{T} \log T) expected regret compared to best weights.

Method identifies low-dimensional structure in high-dimensional probability measures.

problem Identifying low-dimensional structure in high-dimensional probability measures.
method Extends prior work on minimizing majorizations of the Kullback-Leibler divergence to identify optimal approximations within a specific class of measures.
result Connection between dimensional logarithmic Sobolev inequality and approximations with the ansatz.

Lower bounds on MALA and HMC for well-conditioned distributions.

problem Understanding the performance limits of Metropolized sampling methods.
method Analyzing the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator.
result Nearly-tight lower bound of Ω~(κd)\widetildeΩ(κd) on the mixing time of MALA from an exponentially warm start.

We design a randomised parallel version of Adaboost based on previous studies on parallel coordinate descent. The algorithm uses the fact that the logarithm of the exponential loss is a function with coordinate-wise Lipschitz continuous gradient, in order to define the step lengths. We provide the proof of convergence …

2013-10-07abs ↗pdf ↗

We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya wher…

2017-10-23abs ↗pdf ↗

Malicious agents can manipulate linear contextual bandits to pull desired arms with logarithmic overhead.

problem Malicious attacks on linear contextual bandit algorithms in various domains.
method Study and propose an efficient algorithm to perform adversarial attacks on linear contextual bandits.
result Malicious agents can force a linear contextual bandit algorithm to pull any desired arm To(T)T - o(T) times over a horizon of TT steps with logarithmic modifications.

Federated Q-Learning achieves linear regret speedup with low communication cost.

problem Achieving linear regret speedup in federated reinforcement learning without high communication costs.
method Proposed two federated Q-Learning algorithms: FedQ-Hoeffding and FedQ-Bernstein, using event-triggered synchronization, novel step size selection, and concentration inequalities.
result Total regrets achieve linear speedup compared to single-agent counterparts with logarithmic communication cost.

New gradient methods solve multiscale optimization problems efficiently.

problem Minimizing functions with multiple non-interacting smooth, strongly convex components.
method Big-Step-Little-Step interleaving of standard methods.
result Complexity bound scales as product of square-roots of condition numbers of components, improving on accelerated gradient methods.

LMC algorithm converges to target in Chi-squared and Renyi divergence.

problem Sampling from target distribution using LMC with strong dissipativity and smoothness conditions.
method LMC algorithm with strong dissipativity and first-order smoothness, initialized with Gaussian.
result LMC reaches ε-neighborhood of target in Chi-squared and Renyi divergence in O(λ²dε⁻¹) steps.

P. Buser and P. Sarnak showed in 1994 that the maximum, over the moduli space of Riemann surfaces of genus s, of the least conformal length of a nonseparating loop, is logarithmic in s. We present an application of (polynomially) dense Euclidean packings, to estimates for an analogous 2-dimensional conformal systolic i…

2003-02-25abs ↗pdf ↗

Efficient algorithms for sparse parameter recovery in mixture models.

problem Support recovery of high-dimensional sparse latent vectors in mixture models.
method Efficient algorithms with logarithmic sample complexity dependence on dimensionality.
result First guarantees on support recovery for various mixture models.

In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning in subsequent decision steps by directly using sub-trees as action recommender. …

2018-05-03abs ↗pdf ↗

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space. To this e…

2016-05-24abs ↗pdf ↗

New algorithm reduces regret for many bandit algorithms with logarithmic dependence on number of algorithms.

problem Combining and learning over a large set of adversarial bandit algorithms to track the best one.
method Proposes a new algorithm (CORRAL) with logarithmic regret dependence on the number of base algorithms.
result Achieves optimal switching regret for adversarial linear bandits over a dd-dimensional p\ell_p unit-ball.

Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.

problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.

We introduce a new class of reinforcement learning methods referred to as {\em episodic multi-armed bandits} (eMAB). In eMAB the learner proceeds in {\em episodes}, each composed of several {\em steps}, in which it chooses an action and observes a feedback signal. Moreover, in each step, it can take a special action, c…

2015-08-04abs ↗pdf ↗

Study real logarithms of semi-simple matrices, focusing on differential structure.

problem Understanding the differential structure of real logarithms of semi-simple matrices.
method Examines the differential structure of real logarithms of semi-simple matrices under specific matrix types.
result Characterizes the differential structure of real logarithms of semi-simple matrices.

Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.

problem Bounding invariant hypersurfaces and testing log canonicity of singularities.
method Introduce excess logarithmic residues, prove residue formula, derive Poincaré-type bound, and use them to recover log discrepancies.
result Componentwise logarithmic residues of a lifted foliation along the exceptional divisor recover log discrepancies of singularities.

Logarithmic connections on principal bundles over normal varieties are studied.

problem Existence and properties of logarithmic connections on principal bundles over normal varieties.
method Introducing logarithmic connections, showing equivalence to covariant derivatives, and proving existence conditions.
result Existence of logarithmic connections on principal bundles over normal varieties is equivalent to certain conditions on the associated vector bundles and adjoint bundles.

We present a new method to solve certain ˉ\bar{\partial}-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a ˉ\bar{\partial}-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness…

2017-07-31abs ↗pdf ↗

AIHT improves online high-dimensional quantile regression by separating support discovery and refinement.

problem Online high-dimensional quantile regression with structural sparsity.
method Adaptive Iterative Hard Thresholding (AIHT) alternates stochastic updates with adaptive hard-thresholding steps.
result AIHT achieves logarithmic regret for the sliding-window objective in high-dimensional settings.

New insights into how to inspect and learn from multi-stage processes and AI reasoning.

problem Understanding how to attribute outcomes to early stages in multi-stage operations and AI reasoning.
method Information-theoretic analysis and mathematical proofs of four key results.
result Uniform checkpoint spacing is minimax-optimal for inspection design under homogeneous signal attenuation.

Logarithmic separation profile in hyperbolic groups shows hierarchical structure.

problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.

Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.

problem Proving logarithmic Sobolev inequalities on manifolds with nonnegative curvature.
method Employing the ABP method developed by Brendle.
result Sharp L2L^2 and LpL^p logarithmic Sobolev inequalities established.

The paper constructs a Saito basis for a specific class of divisors and applies it to logarithmic Poisson geometry.

problem Investigating a class of non-quasi-homogeneous free divisors and their logarithmic vector fields.
method Explicitly constructing a Saito basis for the module of logarithmic vector fields and applying it to logarithmic Poisson geometry.
result The construction of the Saito basis and the Lie-Rinehart algebra structure on the sheaf of logarithmic 1-forms.