Modern distributed training of machine learning models suffers from high communication overhead for synchronizing stochastic gradients and model parameters. In this paper, to reduce the communication complexity, we propose \emph{double quantization}, a general scheme for quantizing both model parameters and gradients. …
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48 results for “doubling scheme”
AES scheme improves Bermudan and American option pricing for Heston models.
problem Pricing Bermudan and American options under Heston models efficiently.
method AES scheme using non-central chi-square distribution for variance process.
result AES achieves higher accuracy and computational efficiency for Bermudan options.
Hybrid regularization avoids double descent in random feature models.
problem Avoiding the double descent phenomenon in random feature models.
method Combines early stopping and weight decay, using GCV for hyperparameter selection.
result Hybrid method successfully avoids double descent and achieves comparable generalization.
We show that the regular Slodowy slice to the sum of two semisimple adjoint orbits of is isomorphic to the deformation of the -singularity if , the Dancer deformation of the double cover of the Atiyah-Hitchin manifold if , and to the Atiyah-Hitchin manifold itself if . For higher , such…
This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a …
We develop high-order approximations for the Heston model.
problem Modeling the Heston model with high accuracy and efficiency.
method Combining approximation schemes on different random grids to achieve any order of convergence.
result Achieve any order of convergence for the Heston model.
Seidel and Smith have constructed an invariant of links as the Floer cohomology for two Lagrangians inside a complex affine variety Y. This variety is the intersection of a semisimple orbit with a transverse slice at a nilpotent in the Lie algebra We exhibit bijections between a set of generators for the Sei…
The study finds an infinite number of minimal surfaces in 3D spheres.
problem Finding minimal surfaces in 3D spheres.
method Two-parameter min-max scheme in lens spaces, Heegaard foliations flipping.
result Constructs an infinite number of minimal surfaces in .
The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.
problem Characterizing generalization properties of high-dimensional kernel ridge regression.
method Bias-variance decomposition of the expected excess risk, considering different regularization schemes and data eigen-profiles.
result The risk curve of kernel regression can be double-descent-like, bell-shaped, or monotonic, depending on n, d, and regularization level.
Despite the success of single-agent reinforcement learning, multi-agent reinforcement learning (MARL) remains challenging due to complex interactions between agents. Motivated by decentralized applications such as sensor networks, swarm robotics, and power grids, we study policy evaluation in MARL, where agents with jo…
New iterative schemes solve Yamabe-type equations on closed manifolds.
problem Solving Yamabe-type equations on closed manifolds.
method Double iterative scheme and local variational method.
result Reproof of classical Yamabe problem as a consequence of Yamabe-type equations.
New analysis reveals optimal regularization for ESNs, avoiding double descent.
problem Characterizing and optimizing Echo State Networks (ESNs) for precise bias-variance.
method Random matrix theory applied to ESNs in a teacher-student setting.
result ESNs achieve lower MSE with limited training samples and teacher memory.
ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systemsmath.NA
ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.
problem Efficiently simulating ergodic SDEs with large time-steps.
method Inference-based schemes adaptive to large time-steps (ISALT) from data.
result ISALT achieves significant time reduction and optimal accuracy.
Two new algorithms improve Q* approximation in batch RL with linear error propagation.
problem Improving Q* approximation in batch reinforcement learning.
method Two novel algorithms that estimate Bellman error directly, without quadratic dependence.
result Linear-in-horizon error propagation for batch RL algorithms.
Almost sharp local Bernstein estimates for Laplace eigenfunctions on compact Riemannian manifoldsmath.AP
The study sharpens local Bernstein estimates for Laplace eigenfunctions on compact manifolds.
problem Understanding local growth properties of Laplace eigenfunctions on compact Riemannian manifolds.
method Refined Donnelly-Fefferman method based on --Carleman estimates, combined with elliptic regularity and patching of local Carleman estimates.
result Almost sharp local --Bernstein inequalities for .
Study assesses hyperparameter tuning for causal inference with DML.
problem Optimizing hyperparameters for causal inference with DML.
method Empirical simulation study using DML approach.
result Hyperparameter tuning crucial for causal estimation with DML.
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at fixed dates. Our approach yields unbiased estimators with standard deviation in expected time for a variety of processes including the Black-Scholes model, Merton's jump-diffusion mod…
We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a…
New algorithm for multiarmed bandits with variable, unbounded delays achieves similar regret bounds.
problem Variable, unbounded delays in multiarmed bandits.
method Introduces a new algorithm that skips rounds with excessively large delays and uses a doubling scheme.
result Achieves the same regret bound as Exp3 with variable, unbounded delays.
Directly estimates CQC, improving interpretability and accuracy.
problem Inability to model and interpret CQC due to inversion issue.
method Direct doubly robust estimation of CQC without inversion.
result Improved estimation accuracy and interpretability.
Efficient exploration improves large language model performance with fewer queries.
problem Improving large language model performance with fewer human feedback queries.
method Sequentially generates queries, fits a reward model to feedback, uses double Thompson sampling with epistemic neural network uncertainty.
result Efficient exploration enables high performance with far fewer queries.
Joint blind source separation (J-BSS) is an emerging data-driven technique for multi-set data-fusion. In this paper, J-BSS is addressed from a tensorial perspective. We show how, by using second-order multi-set statistics in J-BSS, a specific double coupled canonical polyadic decomposition (DC-CPD) problem can be formu…
We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the fun…
Technical Report: Adaptive Control for Linearizable Systems Using On-Policy Reinforcement Learningcs.LG
Paper proposes adaptive control for unknown systems using reinforcement learning.
problem Adaptive control for unknown, linearizable systems.
method On-policy reinforcement learning for discrete-time, stochastic systems.
result Stability and tracking errors concentrate near zero with high probability.
This work improves variational inference by reducing gradient variance.
problem Hard optimization of flexible variational distributions.
method Control variate based on quadratic approximation of the model's mean and covariance.
result Significant improvement in gradient variance and optimization convergence.
Efficient numerical valuation of European options under the two-asset Kou jump-diffusion modelmath.NA
The paper efficiently solves a complex option valuation equation for two assets.
problem Valuation of European options under a two-asset Kou jump-diffusion model.
method Extends an efficient algorithm for a one-dimensional integral to a two-dimensional one, using operator splitting schemes for time discretization.
result The method achieves optimal computational cost and stable convergence for various operator splitting schemes.
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface is a Klein surface such that there is a degree two morphism (of Klein surfaces) . There are many doubles of a given Klein surface and among them the so-called natural doubles which are: the complex double, the …
Mean field inference in probabilistic models is generally a highly nonconvex problem. Existing optimization methods, e.g., coordinate ascent algorithms, can only generate local optima. In this work we propose provable mean filed methods for probabilistic log-submodular models and its posterior agreement (PA) with stron…
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (…
Data coarse graining can improve model performancecond-mat.stat-mech
Data coarse graining improves model performance by filtering out less relevant features.
problem Lossy data transformations lose information but can improve model generalization.
method Data coarse graining schemes that systematically discard features based on relevance to the learning task.
result A 'high-pass' scheme helps models generalize better by filtering out less relevant features.
The word `double' was used by Ehresmann to mean `an object X in the category of all X'. Double categories, double groupoids and double vector bundles are instances, but the notion of Lie algebroid cannot readily be doubled in the Ehresmann sense, since a Lie algebroid bracket cannot be defined diagrammatically. In this…
Hermite Polynomial-based Valuation of American Options with General Jump-Diffusion Processesq-fin.CP
New method uses Hermite polynomials for American option valuation.
problem Valuation of American options with complex jump-diffusion dynamics.
method Hermite polynomial expansions of transition density and early exercise premium.
result Converging approximations to true option prices and exercise boundaries.
Paper develops a duality approach for robust loss functions in infinite-dimensional RKHSs.
problem Robustness issues in infinite-dimensional RKHSs with operator-valued kernels.
method Develops a duality approach to solve OVK machines for various loss functions.
result Empirical improvements and theoretical stability analysis for robust structured data applications.
Double Principal Bundlesmath.DG
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and conne…
Interpolation improves nearest neighbor algorithms' performance.
problem Improving nearest neighbor algorithms' performance.
method Considered a class of interpolated weighting schemes and characterized their asymptotic performances.
result Mild degree of data interpolation strictly improves prediction accuracy and statistical stability.
Generalizes Hecke algebra for double torus, linking to skein algebra.
problem Understanding algebraic structures on double torus.
method Introducing Heegaard dual operators and Dehn twists.
result Established relationship between Hecke algebra and skein algebra.
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equationsmath.NA
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
problem Positivity-preserving discretizations for anisotropic Fokker-Planck equations
method Diagonal Frog discretization
result Second-order accuracy and mass conservation
Poisson double structuresmath.SG
Introduces Poisson double algebroids and their relation to Lie 2-bialgebras.
problem Developing Lie theory for Poisson double structures.
method Introducing Poisson double algebroids and double Lie bialgebroids, and relating them through differentiation and integration.
result Revisits Lie 2-bialgebras using Poisson double structures.
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor's market participation,…
Survey of global geometry for double field theory.
problem Global description of double field theory geometry.
method Review of Courant algebroids, metric algebroids, AKSZ construction, para-Hermitian geometry.
result Global description of doubled geometry and topological models.
StreaMRAK improves KRR for streaming data.
problem Streaming data with memory constraints.
method Divides problem into levels of resolution, sub-sampling.
result Efficiently integrates new samples, reduces memory and complexity.
This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.
problem Understanding and characterizing transitive double Lie algebroids.
method Using core diagrams and equivalence of transitive core diagrams with transitive double Lie groupoids.
result Transitive double Lie algebroids are completely determined by their core diagrams.
Interpolation improves performance in nearest neighbor algorithms without over-parametrization.
problem Achieving zero training error in deep learning without over-parametrization.
method Introduced a class of interpolated weighting schemes in nearest neighbor algorithms.
result Mild data interpolation strictly improves prediction performance and statistical stability.
We methodologically address the problem of Q-value overestimation in deep reinforcement learning to handle high-dimensional state spaces efficiently. By adapting concepts from information theory, we introduce an intrinsic penalty signal encouraging reduced Q-value estimates. The resultant algorithm encompasses a wide r…
We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as the iterated tangent bundle of an ordinary manifold, and various iterated tangent/cotangent constructions in symplectic and Poisson geometry…
This paper tackles task offloading in edge computing systems with dynamic interactions.
problem Dynamic interactions among mobile users in an edge computing system.
method Modelled as a non-cooperative stochastic game, transformed into a Markov decision process, and solved using online deep reinforcement learning.
result The proposed deep RL scheme balances age of information and energy consumption.
Double L-theorymath.GT
We develop new algebraic methods refining the Witt group of linking forms and Ranicki's torsion algebraic L-groups into double Witt groups and double L-groups. At each prime ideal of the underlying ring, our double Witt groups capture infinitely many more integral signatures of the linking form than the single Witt gro…
Double Affine Bundlesmath.DG
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation and basic examples come from Analytical Mechanics, where double affine bundles hav…