Last-iterate guarantees for learning in co-coercive games under noisy feedback.
problem Learning in co-coercive games with noisy feedback.
method Vanilla stochastic gradient descent with a new noise model.
result Last-iterate bound of order O ( log ( t ) / t 1 / 3 ) O(\log(t)/t^{1/3}) O ( log ( t ) / t 1/3 ) for co-coercive games. 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.
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
Mutation improves FTRL convergence in zero-sum games.
problem Lack of last-iterate convergence in FTRL variants.
method Introduced mutation to perturb action probabilities in FTRL.
result M-FTRL converges to Nash equilibria under full-information feedback.
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…
This paper introduces a new metric, ULI, for RL that ensures both cumulative and instantaneous performance.
problem High-stakes applications require RL algorithms to avoid playing bad policies.
method Introduces uniform last-iterate (ULI) guarantee, a stronger metric capturing both cumulative and instantaneous performance.
result ULI directly implies near-optimal cumulative performance across various metrics, but not the other way around.
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 addresses the convergence of SGD's final iterate without restrictive assumptions.
problem Prove optimal convergence rate of SGD's final iterate without compact domains or bounded noise.
method Unified proof for general domains, composite objectives, non-Euclidean norms, etc.
result First unified convergence rates in expectation and high probability.
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 i l d e O ( T − 1 / 4 ) ilde{O}(T^{-1/4}) i l d e O ( T − 1/4 ) in high probability. SGD achieves near optimal convergence rate in smooth interpolation regime.
problem Optimization of smooth convex objectives with zero noise at optimum.
method Stochastic Gradient Descent (SGD) with large stepsize analysis.
result Last iterate of SGD achieves expected excess risk of O(1/T + σ* / √T) with optimal stepsize.
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) O ( 1/ k ) convergence rates for residual norms. 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.
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.
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.
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.
New study shows faster convergence of SGD and Kaczmarz methods.
problem Improving convergence rates of iterative linear system solvers.
method Last-iterate convergence analysis of SGD with greedy step size over smooth quadratics.
result The t t t -th iterate attains an O ( 1 / t 3 / 4 ) O(1/t^{3/4}) O ( 1/ t 3/4 ) convergence rate. 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 ( T − 1 / 4 ) Ω(T^{-1/4}) Ω ( T − 1/4 ) . result Achieved optimal rate of Ω ( T − 1 / 4 ) Ω(T^{-1/4}) Ω ( T − 1/4 ) for convergence of policy profiles to Nash equilibrium. 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.
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.
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}) O ( 1/ T ) convergence rate for last iterate of both algorithms under componentwise convexity and smoothness. 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.
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) O ( n / k ) and O ( n 2 / k 2 ) \mathcal{O}(n^2/k^2) O ( n 2 / k 2 ) . A new method for RLHF using proximal point Nash learning.
problem Capturing real human preferences in RLHF.
method Proximal point Nash learning, embedding self-play updates into a proximal point framework.
result High-probability last-iterate convergence for the combined method.
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.
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.
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.
New method improves convergence for smooth games.
problem Improving convergence for smooth games.
method Stochastic Hamiltonian Gradient Methods (SHGD).
result SHGD converges linearly to the neighbourhood of a stationary point.
New convergence guarantees for SGDA and SCO under expected co-coercivity.
problem Solving smooth games with stochastic gradient descent-ascent and consensus optimization.
method Introducing expected co-coercivity and proving convergence guarantees for SGDA and SCO.
result Linear convergence of SGDA and SCO to a neighborhood of the solution with constant step-size, and convergence to the exact solution with stepsize-switching rules.
Two accelerated extragradient methods converge at O ( 1 / k ) 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) O ( 1/ k ) last-iterate convergence rates on the residual norm. Motivated by applications in Game Theory, Optimization, and Generative Adversarial Networks, recent work of Daskalakis et al \cite{DISZ17} and follow-up work of Liang and Stokes \cite{LiangS18} have established that a variant of the widely used Gradient Descent/Ascent procedure, called "Optimistic Gradient Descent/Asce…
Meta-algorithm for efficient reinforcement learning from human preferences.
problem Learning from human preference comparisons in Markov decision processes.
method Randomized exploration and experimental design for batch comparison queries.
result Meta-algorithm achieves both regret and last-iterate guarantees with minimal preference queries.
Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.
problem Non-asymptotic bounds for accuracy of normal approximation in linear two-timescale stochastic approximation algorithms.
method Established bounds for normal approximation in terms of convex distance, focusing on last iterate and Polyak-Ruppert averaging.
result Normal approximation rate for the last iterate improves with increased timescale separation, while it decreases in the averaged setting.
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.
Gradient methods converge exponentially in concave network games.
problem Finding Nash equilibria in concave network zero-sum games.
method Gradient Ascent and Optimistic Gradient Ascent analyses.
result Exponential convergence rates in various game settings.
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.
Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.
problem Optimizing convex and Lipschitz functions with heavy-tailed noise.
method Develops tail bounds for optimization error of Stochastic Mirror Descent.
result Tail bounds extend to heavier-tailed noise regimes without diameter constraints.
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…
Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk management due to its simplicity and interpretability. Existing algorithms for mean-…
In this paper, we consider unregularized online learning algorithms in a Reproducing Kernel Hilbert Spaces (RKHS). Firstly, we derive explicit convergence rates of the unregularized online learning algorithms for classification associated with a general gamma-activating loss (see Definition 1 in the paper). Our results…
Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.
problem Approximately solving linear fixed point equations with Markovian data.
method Non-asymptotic bounds and instance-dependent characterizations for stochastic approximation.
result Instance-optimality of the averaged SA estimator and matching upper and lower bounds.
Paper learns Koopman operator from sparse data, escaping function space constraints.
problem Learning Koopman operator from non-closed function spaces.
method Operator stochastic approximation algorithm using conditional mean embeddings (CME).
result Online sparse learning algorithm with trajectory-based sampling guarantees.
New NPG variants ensure parameter convergence in multi-agent learning.
problem Non-convergence of parameters in NPG for multi-agent learning.
method Proposed variants of NPG for multi-agent learning scenarios.
result Global last-iterate parameter convergence guarantees in various multi-agent learning settings.
New UCB algorithm for learning PSRs with tractable computation and accuracy.
problem Learning predictive state representations in sequential decision-making problems.
method Proposes a novel UCB-type algorithm with a bonus term to estimate PSRs accurately and efficiently.
result First known UCB-type approach for PSRs with guaranteed model accuracy and computational tractability.
In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors of VR-SGD are set to the average and last iterate of the previous epoch, respecti…
New algorithm achieves sublinear regret in CMDPs without error cancellations.
problem Safety constraints in reinforcement learning with error cancellations.
method Model-based primal-dual algorithm for CMDPs with multiple constraints.
result Achieves sublinear regret without error cancellations.
The paper shows how data and algorithm interactions affect overparameterized linear regression generalization.
problem Understanding generalization in overparameterized linear regression.
method Introducing data-algorithm compatibility and performing data-dependent trajectory analysis with gradient descent.
result Early stopping iterates lead to better generalization than last-iterate analysis, with weaker restrictions.
ROOT-SGD solves convex optimization problems with optimal nonasymptotic and near-optimal asymptotic performance.
problem Solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms.
method ROOT-SGD: Recursive One-Over-T SGD, averaging past stochastic gradients.
result Achieves state-of-the-art performance in both nonasymptotic and asymptotic senses.
SGD converges to optimal solution in perfect data fitting problem.
problem Noiseless least-squares with perfect data fitting.
method Last iterate of SGD with constant step-size.
result Convergence of SGD final iterate for non-strongly convex problem.