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 λ λ λ -cocoercive games and develops adaptive algorithms. result Adaptive algorithms achieve same convergence rates as non-adaptive counterparts.
Finite-precision learning of a n h anh anh networks is limited by the Monte Carlo rate.
problem Learning a n h anh anh neural networks under finite precision method Using iterated a n h anh anh activations to construct localized bump functions result No adaptive randomized algorithm can achieve higher convergence rate than Monte Carlo rate in finite precision
This paper analyzes momentum Q-learning with finite-sample guarantees.
problem Improving Q-learning performance with momentum schemes.
method Proposes MomentumQ algorithm integrating Nesterov and Polyak's momentum schemes, analyzes convergence for function approximations.
result Establishes finite-sample convergence rates for MomentumQ, demonstrating better performance than vanilla Q-learning.
We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the learning rate is fixed. The key idea in obtaining these bounds is to use a Lyapunov fun…
This study analyzes communication constraints in MoE architectures using information theory.
problem Communication constraints in Mixture-of-Experts (MoE) architectures.
method Developed a rate-distortion characterization of finite-rate gating in MoE architectures using information theory.
result Yielded capacity-aware limits for communication-constrained MoE systems.
Analyzes symmetries in neural networks to predict learning dynamics.
problem Understanding the dynamics of neural network parameters during training.
method Unified theoretical framework based on symmetries and conservation laws.
result Symmetries impose geometric constraints on gradients and Hessians, leading to conservation laws.
A new topology improves decentralized learning efficiency and accuracy.
problem Finding efficient decentralized learning topologies with fast consensus and low maximum degree.
method Proposed the Base- ( k + 1 ) (k + 1) ( k + 1 ) Graph topology for decentralized learning. result The Base- ( k + 1 ) (k + 1) ( k + 1 ) Graph enables faster convergence and better communication efficiency than the exponential graph. SGDM accelerates faster than SGD with large batch sizes and permits broader learning rates.
problem Understanding the role of momentum in SGDM and its convergence rates.
method Analysis of SGDM convergence rates under strongly convex settings, including finite-sample rates and asymptotic normality of the averaged estimator.
result SGDM converges faster than SGD with large batch sizes and permits broader learning rates.
The paper analyzes reinforcement learning methods for estimating weights and quality functions with fast convergence rates.
problem Estimating weights and quality functions in reinforcement learning with function approximation.
method The paper uses minimax methods for estimating marginal importance weights and q-functions.
result The minimax approach enables fast rates of convergence for weights and quality functions, achieving first-order efficiency.
The paper clarifies the approximation of SGD with Ito SDEs for finite learning rates.
problem Theoretical justification and experimental verification of the Ito SDE approximation for finite learning rates in SGD.
method An efficient simulation algorithm SVAG and a necessary condition test for the SDE approximation.
result The Ito SDE approximation can meaningfully capture training and generalization properties of deep nets with finite learning rates.
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
problem Improving option pricing accuracy in volatile financial markets.
method Extended Black-Scholes model using finite difference method and LSTM machine learning.
result Finite difference method outperforms LSTM in computational efficiency but not in accuracy.
Study the properties of SGD in non-vanishing learning rate regime.
problem Understanding the noise and fluctuation in SGD with finite learning rates.
method Derive exact solvable results for discrete-time SGD in quadratic loss functions.
result Fluctuation caused by discrete-time dynamics is larger than continuous-time theory predicts.
Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a…
We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of theoretical analyses of deep learning has revealed its high expressive power and unive…
The paper analyzes GTD algorithms with finite-sample bounds.
problem Convergence rate analysis of GTD family of algorithms.
method Formulated as stochastic gradient algorithms and analyzed using saddle-point error.
result Obtained finite-sample bounds on GTD performance.
Improved TD learning with tail averaging and regularization achieves optimal convergence rates.
problem Convergence analysis of TD learning with linear function approximation.
method Tail-averaging and regularization applied to TD learning algorithm.
result Achieves optimal O ( 1 / t ) O(1/t) O ( 1/ t ) convergence rate in expectation and with high probability. Study on distributional TD learning with linear approximations for better return estimation.
problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.
A theorem for debiasing machine learning with finite sample guarantees.
problem Calculating confidence intervals for machine learning functionals.
method Debiased machine learning based on bias correction and sample splitting.
result Nonasymptotic debiased machine learning theorem with finite sample guarantees.
Paper studies MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.
problem Analyzing MCCR models with scale parameters approaching zero.
method Investigates MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.
result Optimal learning rate of MCCR models is O ( n − 1 ) {\mathcal{O}}(n^{-1}) O ( n − 1 ) in the asymptotic sense. Large learning rates work surprisingly well in standard parameterization, contrary to theory.
problem Theoretical limits of large learning rates do not match practical network behavior.
method Fine-grained analysis of learning rates and network behavior under cross-entropy loss.
result There are two distinct sub-regimes of unstable learning rates, with a controlled divergence regime where features continue to evolve.
Study learns dynamics of linear systems from multiple short trajectories.
problem Learning dynamics of autonomous linear systems from multiple short trajectories.
method Finite sample analysis for stable and unstable systems, adjusting trajectory length for marginally stable systems.
result Learning rate of O ( 1 N ) \mathcal{O}(\frac{1}{\sqrt{N}}) O ( N 1 ) for both stable and unstable systems. New bounds for SA with arbitrary norm contractions and Markovian noise.
problem Finite-time analysis of two-time-scale stochastic approximation with arbitrary norm contractions and Markovian noise.
method Use of generalized Moreau envelope for arbitrary norm contractions and solutions of Poisson equation for Markovian noise.
result Mean square error decays at rates of O ( 1 / n 2 / 3 ) O(1/n^{2/3}) O ( 1/ n 2/3 ) and O ( 1 / n ) O(1/n) O ( 1/ n ) under different conditions. New algorithm optimizes beam and rate allocation in mmWave systems for multiple users.
problem Optimizing beam and rate allocation in mmWave systems for multiple users with limited feedback.
method Introducing SAT-CTS, a combinatorial semi-bandit policy with satisficing objective.
result SAT-CTS achieves finite-time regret bounds and reduces satisficing regret in mmWave systems.
We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class-conditiona…
Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on stationary problems, and permitting learning rates to grow appropriately in non-stati…
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
Two new Frank-Wolfe algorithms improve convergence for constrained optimization.
problem Solving optimization problems with structured constraints in machine learning.
method Two new variants of the Frank-Wolfe (FW) method for stochastic finite-sum minimization.
result Best convergence guarantees for convex and non-convex objective functions.
Policy gradient algorithm with variable learning rates achieves near-optimal performance in multi-arm bandit problems.
problem Optimizing a policy gradient algorithm for multi-arm bandit problems with variable learning rates.
method Applied Foster-Lyapunov techniques to analyze a Markov chain formed by the state of the algorithm.
result The policy gradient algorithm converges to the optimal arm with logarithmic or poly-logarithmic regret.
Learning rates for least-squares regression are typically expressed in terms of L 2 L_2 L 2 -norms. In this paper we extend these rates to norms stronger than the L 2 L_2 L 2 -norm without requiring the regression function to be contained in the hypothesis space. In the special case of Sobolev reproducing kernel Hilbert spaces used …
Paper analyzes finite-time convergence of double Q-learning.
problem Overestimation issue in Q-learning.
method Finite-time analysis of double Q-learning.
result Convergence to ε-accurate neighborhood in finite iterations.
New insights into how large learning rates affect transformer training dynamics.
problem Understanding how large learning rates impact the training of transformer models.
method Analyzing a simplified linear transformer model with a two-factor product map.
result Large learning rates can lead to various training outcomes including cycles, chaos, or divergence.
SGD with large learning rates can achieve better test accuracy than expected.
problem SGD with large learning rates often outperforms expected convergence bounds.
method Proved that SGD with small learning rates stays close to gradient flow path on modified loss.
result Explicitly adding an implicit regularizer to the loss improves test accuracy.
Study non-parametric frequency-domain system identification from finite samples.
problem Frequency-domain system identification from limited data.
method Empirical Transfer Function Estimate (ETFE) under sub-Gaussian colored noise and stability assumptions.
result ETFE estimates are concentrated around true values with a finite-sample rate of N t o t − 1 / 3 N_{\mathrm{tot}}^{-1/3} N tot − 1/3 for all frequencies in the H ∞ \mathcal{H}_{\infty} H ∞ norm. Paper analyzes TD( λ λ λ ) convergence rates for arbitrary features.
problem Convergence rates for linear TD( λ λ λ ) under arbitrary features. method Developed a novel stochastic approximation result for arbitrary features.
result Established L 2 L^2 L 2 convergence rates for linear TD( λ λ λ ) without linearly independent features assumption. Paper analyzes convergence rates of two time-scale AC and NAC algorithms.
problem Finite-sample convergence rate analysis of two time-scale AC and NAC algorithms.
method Developed novel techniques for bias error and convergence rate analysis.
result Established non-asymptotic convergence rates for two time-scale AC and NAC.
Study on optimal rates for sequential probability assignment using smoothed analysis.
problem Optimal rates for sequential probability assignment under smoothed adversaries.
method General-purpose reduction from minimax rates to transductive learning, development of an efficient algorithm using MLE oracle.
result Optimal (logarithmic) fast rates for parametric and finite VC dimension classes, sublinear regret for general classes.
Maximizes coding rate difference for robust, discriminative features.
problem Learning robust, discriminative features from high-dimensional data.
method Maximal Coding Rate Reduction (MCR^2) principle.
result Significantly more robust to label corruptions in classification.
Gradient descent-ascent converges to strict local minmax equilibria with a finite timescale separation.
problem Analyzing the convergence of gradient descent-ascent in non-convex, non-concave games with a finite timescale separation.
method Investigates the role of a finite timescale separation parameter τ on gradient descent-ascent in two-player zero-sum games, providing convergence rates and non-convergence results.
result Gradient descent-ascent converges to strict local minmax equilibria for a finite timescale separation parameter τ*.
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…
Unified analysis for shuffling-type gradient methods in optimization.
problem Optimization of finite-sum problems using shuffling strategies.
method Unified convergence analysis for various shuffling methods.
result Improved convergence rates for nonconvex problems and matching rates for convex problems.
Study pricing of American put options with stochastic interest rate and finite maturity.
problem Pricing American put options with stochastic interest rate and finite maturity.
method Applied stochastic calculus and Ito's lemma to derive the option value's formula and optimal exercise boundary.
result Existence and parametrisation of the optimal exercise boundary for the Vasicek model.
SMG combines shuffling and momentum for non-convex optimization.
problem Non-convex finite-sum optimization problems.
method Shuffling Gradient-based method with momentum.
result Established state-of-the-art convergence rates for SMG.
Privacy affects how much data is needed for CVaR optimization.
problem Privacy constraints impact the effective sample size for CVaR optimization.
method Analyzes the privacy-relevant sample size and decomposes CVaR excess risk.
result The effective private tail sample size is εnτ, affecting CVaR learning rates.
Study optimizes learning rates for conditional mean embedding estimates.
problem Consistency of kernel ridge regression for conditional mean embedding.
method Adaptive statistical learning rate derived for misspecified setting.
result Upper bound matches optimal O ( log n / n ) O(\log n / n) O ( log n / n ) rates without assuming finite dimensionality. New algorithms robustly estimate mean with near-optimal error rates.
problem Outlier robust mean estimation in high-dimensional data.
method Stability condition and iterative filtering algorithms.
result Optimal error rates with subgaussian rates for robust mean estimation.
The paper simplifies multi-agent RL dynamics in finite-state Markov games using homogenization.
problem Approximating complex multi-agent reinforcement learning dynamics in finite-state Markov games.
method Rescaling learning process by reducing learning rate and increasing update frequency, proving convergence to an ODE.
result The rescaled process converges to an ODE that approximates the agent's learning dynamics.
GANs learn distributions well from samples, with rates depending on intrinsic dimension.
problem Learning distributions from samples using GANs.
method Oracle inequality, Hölder functions approximation, neural network approximation, integral probability metrics.
result Convergence rates of GANs depend on intrinsic dimension, not ambient dimension.
This work analyzes Q Q Q -learning with adaptive stepsizes for finite-time convergence.
problem Finite-time convergence analysis for average-reward Q Q Q -learning with adaptive stepsizes. method Adaptive stepsizes as local clocks, time-inhomogeneous Markovian reformulation, almost-sure time-varying bounds, conditioning arguments, and Markov chain concentration inequalities.
result Convergence rates of i l d e O ( 1 / k ) ilde{\mathcal{O}}(1/k) i l d e O ( 1/ k ) for mean-square and pointwise mean-square convergence.