Constant-Stepsize Stochastic Approximation: Finite-Time Convergence, Gaussian Approximation, and Tail Bounds

arXiv:2602.13960 · cs.LG, math.PR · Submitted 2026-02-15 · Read on arXiv

cs.LG, math.PR

Submitted: 2026-02-15

Updated: 2026-09-08

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Objective Function — 10× in this paper · explained in 2 episodes
• Wasserstein Distance — 10× in this paper · explained in 4 episodes
• Central Limit Theorem — 8× in this paper
• Reinforcement Learning — 8× in this paper · explained in 4 episodes
• Q-learning — 4× in this paper · explained in 3 episodes
• Verification — 4× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Adaptive Algorithm — 2× in this paper · explained in 1 episode
• Core — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Temporal Correlations — 2× in this paper · explained in 2 episodes
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Elias — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• Lyapunov function — 1× in this paper · explained in 2 episodes
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Reinforcement Learning (RL) — 1× in this paper · explained in 24 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Efficient Concentration with Gaussian Approximation
• On the diffusion approximation of nonconvex stochastic gradient descent
• Stochastic Approximation with Unbounded Markovian Noise: A General-Purpose Theorem
• Proximal Policy Optimization Algorithms
• Quantitative Error Bounds for Scaling Limits of Stochastic Iterative Algorithms

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