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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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108215323430 · Jun 202019922001200920172026
48 results for Last Iterate Convergence

Last iterate of Extragradient algorithm converges slower than averaged iterates in saddle point problems.

problem Smooth convex-concave saddle point problems
method Analysis of Extragradient (EG) algorithm convergence rates
result The last iterate of EG converges at a rate of O(1/√T), compared to O(1/T) for averaged iterates

OMWU shows last iterate convergence in convex-concave games.

problem Optimizing in constrained min-max optimization landscapes.
method OMWU (Optimistic Multiplicative-Weights Update) in the no-regret online learning framework.
result OMWU exhibits last iterate convergence for convex-concave games, generalizing previous results.

New convergence rates for shuffling gradient methods without strong convexity.

problem Theoretical gap between shuffling gradient methods' empirical success and established convergence rates.
method Proved last-iterate convergence rates for shuffling gradient methods using function value gap.
result First last-iterate convergence rates for shuffling gradient methods without strong convexity.

While classic work in convex-concave min-max optimization relies on average-iterate convergence results, the emergence of nonconvex applications such as training Generative Adversarial Networks has led to renewed interest in last-iterate convergence guarantees. Proving last-iterate convergence is challenging because ma…

2019-06-05abs ↗pdf ↗

Improved convergence rates for saddle-point optimization algorithms.

problem Understanding last-iterate convergence rates for saddle-point optimization algorithms in constrained settings.
method Expanding the understanding of last-iterate convergence for Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative Weights Update (OMWU) in the constrained setting.
result Linear last-iterate convergence achieved with a universal constant learning rate for OMWU in bilinear games over the simplex.

Paper proves suboptimal convergence rate of last iterate for SGDM.

problem Proves suboptimal convergence rate of last iterate for SGDM.
method Focuses on convergence rate of last iterate of SGDM, introduces Follow-The-Regularized-Leader-based algorithms.
result Shows optimal convergence rate of last iterate for unconstrained convex stochastic optimization problems.

Optimizes convergence rate of stochastic proximal algorithms for composite convex problems.

problem Solving composite convex optimization problems with composite regularizers.
method Analyzed proximal stochastic gradient method and randomized incremental proximal method under relaxed variance assumptions.
result Proves O(1/T)O(1/\sqrt{T}) convergence rate for last iterate of both algorithms under componentwise convexity and smoothness.

New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.

problem Analyzing convergence properties of saddle-point optimization methods.
method High-Resolution Differential Equations (HRDEs) to design differential equation models for saddle-point optimization methods.
result HRDEs reveal last-iterate convergence for Optimistic Gradient Descent Ascent (OGDA) in bilinear games.

Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.

problem Learning dynamics in bilinear saddle-point problems with bandit feedback.
method Uncoupled learning algorithm combining experimental design and FTRL with a tailored regularizer.
result Last-iterate convergence rate of ildeO(T1/4) ilde{O}(T^{-1/4}) in high probability.

Paper analyzes convergence rates for multi-agent learning in games.

problem Convergence rates for multi-agent learning in games.
method Characterizes finite-time convergence rates for joint OGD learning on λλ-cocoercive games and develops adaptive algorithms.
result Adaptive algorithms achieve same convergence rates as non-adaptive counterparts.

Improved shuffling gradient methods converge faster for nonsmooth convex optimization.

problem Improving convergence rates for nonsmooth convex optimization problems.
method Analysis of shuffling gradient methods, focusing on Random Reshuffle and Single Shuffle strategies.
result Shuffling gradient methods, particularly Random Reshuffle and Single Shuffle, converge faster than Proximal Gradient Descent for nonsmooth convex optimization.

This paper advances extragradient methods for solving inclusions under co-hypomonotonicity.

problem Solving inclusions with non-Lipschitz mappings.
method Unified and generalized extragradient methods under co-hypomonotonicity.
result Achieved O(1/k)\mathcal{O}(1/k) convergence rates for residual norms.

Two accelerated extragradient methods converge at O(1/k)O(1/k) rate for co-hypomonotone inclusions.

problem Solving co-hypomonotone inclusions with sum of Lipschitz and multivalued operators.
method Developed two Nesterov's accelerated extragradient methods for co-hypomonotone inclusions.
result Achieve O(1/k)\mathcal{O}(1/k) last-iterate convergence rates on the residual norm.

The paper analyzes convergence rates for SGD and SHB methods.

problem Analyzing convergence rates for stochastic gradient descent and heavy ball methods.
method Stochastic gradient descent and stochastic heavy ball method for general stochastic approximation problems.
result The last iterate of SHB converges almost surely to a minimizer and has faster convergence rates than SGD.

Algorithm converges to Nash equilibria in competitive games.

problem Finding Nash equilibria in decentralized, competitive Markov games.
method Decentralized Optimistic Gradient Descent/Ascent with a critic.
result Converges to the set of Nash equilibria under self-play.

In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially decaying step size in each iteration can play a role of regularization to ensure the generalizati…

2017-10-10abs ↗pdf ↗

New algorithms converge faster to Nash equilibrium in zero-sum games with bandit feedback.

problem Learning in zero-sum games with bandit feedback without communication.
method Developed two uncoupled algorithms achieving optimal rate of Ω(T1/4)Ω(T^{-1/4}).
result Achieved optimal rate of Ω(T1/4)Ω(T^{-1/4}) for convergence of policy profiles to Nash equilibrium.

Improved SEG method converges to Nash equilibrium in bilinear games.

problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.

Last SGD iterate bounds for overparameterized linear regression.

problem Analyzing the last iterate risk bounds of SGD with decaying stepsize for overparameterized linear regression.
method Problem-dependent analysis of last iterate risk bounds of SGD with geometrically decaying stepsize.
result Proved nearly matching upper and lower bounds on the excess risk for last iterate SGD with geometrically decaying stepsize.

Non-affine aggregation rules cannot preserve monotonicity in convex learning.

problem Designing non-affine aggregation rules that maintain monotonicity in convex learning.
method Proving that monotonicity of aggregated gradients is preserved only if the aggregation rule is positively affine.
result Non-affine aggregation prevents steady convergence and substantially degrades algorithmic stability.

Unified algorithm solves convex optimization problems with optimal rates.

problem Solving nonsmooth constrained convex optimization problems.
method Unified randomized block-coordinate primal-dual algorithm.
result Achieves optimal convergence rates of O(n/k)\mathcal{O}(n/k) and O(n2/k2)\mathcal{O}(n^2/k^2).

Value aggregation is a general framework for solving imitation learning problems. Based on the idea of data aggregation, it generates a policy sequence by iteratively interleaving policy optimization and evaluation in an online learning setting. While the existence of a good policy in the policy sequence can be guarant…

2018-01-22abs ↗pdf ↗

Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update w…

2019-10-08abs ↗pdf ↗

New privacy bounds for DP-SGD's last iterate, even with cyclic sampling.

problem Privacy of the last iterate in DP-SGD with cyclic sampling.
method Established new RDP upper bounds for the last iterate under realistic assumptions.
result Privacy bounds for DP-SGD's last iterate with cyclic sampling and clipping, even for nonconvex losses.

This work provides formal guarantees for heuristic optimization methods in machine learning.

problem Lack of theoretical understanding of heuristic optimization methods in machine learning.
method Analysis and formal guarantees for AdaGrad, SGD with exponential and cosine step sizes, and momentum methods.
result First formal guarantees for AdaGrad and SGD variants, including convergence and adaptivity to noise.

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most first-order methods only guarantee an ergodic convergence rate, that is, the uniform…

2019-03-26abs ↗pdf ↗

Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation. In this paper, we study the selection of adapted step sizes for ISTA. We show t…

2019-05-27abs ↗pdf ↗

This paper resolves BIHT convergence, showing normalization is not necessary in noiseless settings but crucial for robustness.

problem Analyzing convergence and robustness of BIHT for 1-bit compressed sensing.
method Characterizes BIHT convergence and robustness, proving necessity of normalization for robustness under sign corruptions.
result Per-iteration normalization is not necessary for optimal recovery in noiseless settings but is crucial for robustness under sign corruptions.

Paper generalizes extragradient methods for solving equations and inclusions with improved convergence rates.

problem Solving equations and inclusions using extragradient methods.
method Unified and generalized extragradient methods for a broader class of algorithms, analyzing sublinear convergence rates.
result Unified and improved convergence results for various extragradient variants.

Survey on extragradient methods for solving nonlinear equations and inclusions.

problem Approximating solutions of nonlinear equations and inclusions.
method Unified convergence analysis of extragradient and its variants.
result Sublinear convergence rates for different classes of algorithms.

New algorithm for solving minimax problems over distributions converges to Nash equilibrium.

problem Solving minimax problems over probability distributions.
method Symmetric Mean-field Langevin Dynamics (MFL-AG and MFL-ABR) with weighted averaging and best response dynamics.
result Converges to mixed Nash equilibrium with average-iterate and last-iterate convergence.

Study on SGD for overparameterized neural networks, focusing on convergence rates.

problem Understanding convergence rates of SGD in overparameterized two-layer neural networks.
method Combines NTK approximation with RKHS analysis to explore SGD dynamics.
result Established sharp convergence rates for SGD in overparameterized two-layer neural networks.

Develops new algorithms for solving root-finding problems in large-scale settings.

problem Solving nonlinear equations in large-scale settings.
method Randomized block-coordinate optimistic gradient algorithms.
result Achieves convergence rates of O(1/k)\mathcal{O}(1/k) and O(1/k2)\mathcal{O}(1/k^2) for root-finding problems.

WSqD extends learning rate schedules for large model training without fixed horizons.

problem Fixed learning rate schedules limit training horizon extension.
method WSqD replaces constant stable phase with a shifted inverse-square-root base, retaining linear cooldown.
result WSqD achieves minimax-optimal convergence rate and horizon-independence.

The paper analyzes Q-learning convergence rates with asynchronous updates.

problem Analyzing convergence rates of asynchronous Q-learning algorithms.
method Derives rates of convergence using high-dimensional central limit theorems.
result Establishes a rate of order up to n1/6log4(nSA)n^{-1/6} \log^{4} (nS A) for hyper-rectangles.

Counterfactual Regret Minimization (CFR) has found success in settings like poker which have both terminal states and perfect recall. We seek to understand how to relax these requirements. As a first step, we introduce a simple algorithm, local no-regret learning (LONR), which uses a Q-learning-like update rule to allo…

2019-10-07abs ↗pdf ↗

Paper develops Gaussian approximations and bootstrap for federated LSA with trade-off bounds.

problem Analyzing convergence rates and trade-offs in federated linear stochastic approximation.
method Established Berry-Esseen-type bounds for federated LSA, developed multiplier bootstrap for inference.
result First federated Gaussian approximations with explicit trade-off terms and non-asymptotic validity guarantees.