In this paper we present a framework to analyze the asymptotic behavior of two timescale stochastic approximation algorithms including those with set-valued mean fields. This paper builds on the works of Borkar and Perkins & Leslie. The framework presented herein is more general as compared to the synchronous two times…
This study improves convergence of two-timescale SA under Markovian noise in reinforcement learning.
problem Stability and convergence of two-timescale stochastic approximations under Markovian noise.
method Introduced a new control strategy for the fast timescale parameter.
result Established almost sure convergence of TDC with eligibility traces under off-policy learning with linear function approximation.
Proves convergence of neural networks in a two-timescale regime.
problem Training dynamics of shallow neural networks.
method Two-timescale regime analysis of gradient flow.
result Gradient flow converges to global optimum in non-convex optimization.
Paper analyzes Greedy-GQ for reinforcement learning with Markovian noise.
problem Analyzing Greedy-GQ for reinforcement learning with Markovian noise.
method Develops finite-sample analysis for Greedy-GQ with linear function approximation under Markovian noise.
result Provides theoretical justification for choosing stepsizes for faster convergence.
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.
This paper analyzes the sample complexity of two timescale reinforcement learning algorithms.
problem Analyzing the sample complexity of two timescale reinforcement learning algorithms.
method Non-asymptotic analysis of linear and nonlinear TDC and Greedy-GQ algorithms under Markovian sampling with constant stepsize.
result The paper provides non-asymptotic convergence results for two timescale linear and nonlinear TDC and Greedy-GQ algorithms.
Study on Adam-family methods for nonsmooth optimization with convergence guarantees.
problem Training nonsmooth neural networks with convergence guarantees.
method Two-timescale updating scheme and stochastic subgradient methods with gradient clipping.
result Convergence guarantees for various Adam-family methods in training nonsmooth neural networks.
Study analyzes a new algorithm for complex optimization problems.
problem Stochastic bilevel optimisation problems in continuous-time models.
method Continuous-time, two-timescale stochastic approximation algorithm.
result Obtained weak convergence rate using central limit theorem.
We present the first provably convergent two-timescale off-policy actor-critic algorithm (COF-PAC) with function approximation. Key to COF-PAC is the introduction of a new critic, the emphasis critic, which is trained via Gradient Emphasis Learning (GEM), a novel combination of the key ideas of Gradient Temporal Differ…
Linear two-timescale stochastic approximation (SA) scheme is an important class of algorithms which has become popular in reinforcement learning (RL), particularly for the policy evaluation problem. Recently, a number of works have been devoted to establishing the finite time analysis of the scheme, especially under th…
Two-Timescale EM Methods improve EM for nonconvex models.
problem Nonconvex latent variable models are challenging for EM.
method Two-stage stochastic updates to handle nonconvex optimization.
result Global convergence for nonconvex objective functions.
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Paper analyzes CLT for TTSA with Markovian noise, broadening its applications.
problem Analyzing asymptotic behavior of TTSA under Markovian noise.
method Central Limit Theorem applied to TTSA with Markovian noise.
result Uncovered coupled dynamics of TTSA influenced by Markov chain.
The paper analyzes the sample complexities for policy evaluation with linear function approximation.
problem Policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes.
method Investigates sample complexities for two policy evaluation algorithms: TD and TDC.
result Establishes high-probability sample complexity bounds for policy evaluation algorithms.
This work analyzes how neural networks learn representations in actor-critic algorithms.
problem Theoretical support for neural AC algorithms is limited to linear function approximations.
method Mean-field analysis of a two-timescale learning AC algorithm with overparameterized networks.
result Neural AC finds the globally optimal policy at a sublinear rate in the continuous-time and infinite-width limiting regime.
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise components in addition to martingale difference noise. We analyze the asymptotic…
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of a…
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…
Authors improve accuracy analysis for portfolio optimization with multiple timescale factors.
problem Asymptotic accuracy of portfolio optimization approximations for general utility functions and two timescale factors.
method Construct sub- and super-solutions to fully nonlinear problem.
result Rigorous justification of accuracy for portfolio optimization with general utility functions and two timescale factors.
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we propose an actor-critic reinforcement learning algorithm that provably converges t…
New analysis improves understanding of bilevel optimization stability and generalization.
problem Understanding how well bilevel optimization algorithms generalize.
method Algorithmic stability arguments and generalization bounds for three bilevel minimax solvers.
result Precise trade-off between algorithmic stability, generalization gaps, and practical settings.
New IRL algorithm identifies optimal reward and policy from expert demonstrations.
problem Understanding reward functions from expert demonstrations with neural networks.
method Two-timescale single-loop IRL algorithm for neural network parameterized rewards.
result First IRL algorithm with non-asymptotic convergence guarantee and global optimality in neural network settings.
Two-layer neural networks learn efficiently using kernel methods in mean-field analysis.
problem Feature learning ability of two-layer neural networks in the mean-field regime.
method Mean-field analysis through kernel methods, focusing on dynamics of the first layer's kernel.
result Two-layer neural networks can learn a union of multiple reproducing kernel Hilbert spaces more efficiently than kernel methods.
Two novel algorithms improve distributed machine learning in the presence of Byzantine adversaries.
problem Improving distributed machine learning in the presence of Byzantine adversaries.
method Two novel stochastic gradient descent algorithms, ByGARS and ByGARS++, using reputation scores for gradient aggregation.
result Robust to any number of multiplicative noise Byzantine adversaries and converge for strongly convex loss functions.
The paper analyzes an actor-critic algorithm with target networks for deep reinforcement learning.
problem Lack of theoretical understanding of target networks in actor-critic methods.
method Proposes a theoretical analysis of an online target-based actor-critic algorithm with linear function approximation.
result Establishes asymptotic convergence results and finite-time analysis for both critic and actor.
Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.
problem Learning dynamics in zero-sum polymatrix games under different information settings.
method Two-timescale learning dynamics combining smoothed best-response updates and TD-learning for estimating local payoff functions.
result Polynomial-time finite-sample guarantees for convergence to an ε-Nash equilibrium in the minimal information case.
Study improves distributed linear estimation under adversarial conditions.
problem Mean estimation of a random vector with adversarial measurements and asynchrony.
method Two-timescale ℓ1-minimization algorithm with tight convergence rates.
result Unified finite-time characterization of robustness, identifiability, and statistical efficiency.
Paper analyzes Transformer learning dynamics, proving benign landscape for in-context learning.
problem Understanding how Transformers learn in context with nonlinear features.
method Mean-field and two-timescale analysis of Transformer dynamics, proving nonconvex but benign landscape.
result Proves mean-field dynamics avoid saddle points, leading to improved optimization.
Gradient flow solves multi-index regression for high-dimensional Gaussian data.
problem Learning multi-index functions from high-dimensional Gaussian data.
method Two-timescale algorithm with non-parametric link function learning.
result Global convergence of Grassmannian population gradient flow dynamics.
Develops a new method for efficient stochastic bilevel optimization.
problem Stochastic bilevel optimization problems in machine learning applications.
method Single-Timescale stochAstic BiLevEl optimization (STABLE) method.
result Achieves the same order of sample complexity as stochastic gradient descent for single-level optimization.
Single-timescale actor-critic finds globally optimal policy.
problem Finding globally optimal policy in reinforcement learning.
method Simultaneous actor and critic updates with linear or deep neural network approximations.
result Actor sequence converges to globally optimal policy at O(K−1/2) rate. SUSTAIN algorithm tackles stochastic bilevel optimization with near-optimal complexity.
problem Stochastic bilevel optimization problems with specific convexity and smoothness properties.
method SUSTAIN algorithm using single-timescale double-momentum stochastic approximation.
result SUSTAIN achieves near-optimal complexity for finding ε-stationary solutions.
We study the detailed path-wise behavior of the discrete-time Langevin algorithm for non-convex Empirical Risk Minimization (ERM) through the lens of metastability, adopting some techniques from Berglund and Gentz (2003. For a particular local optimum of the empirical risk, with an arbitrary initialization, we show tha…
Two single-timescale algorithms improve TD learning with nonlinear approximations.
problem Optimizing TD learning with nonlinear smooth function approximation.
method Proposes two single-timescale single-loop algorithms with momentum and variance reduction.
result Achieves O(ε−4) sample complexity for the first algorithm and O(ε−3) for the second. New algorithm reduces bias in off-policy reinforcement learning.
problem Challenges in designing off-policy reinforcement learning algorithms.
method Doubly robust off-policy actor-critic (DR-Off-PAC) with a single timescale structure.
result Establishes the first overall sample complexity analysis for a single time-scale off-policy AC algorithm.
PFedRL-Rep learns shared and personalized policies for heterogeneous environments.
problem Poor performance of single policy in heterogeneous environments.
method Develops PFedRL-Rep framework with shared feature representation and personalized weights.
result Proves linear convergence speedup with respect to the number of agents.
Semi-decentralized federated learning combines device-to-server and device-to-device communications for faster convergence.
problem Faster convergence in federated learning with decentralized model training.
method Two timescale hybrid federated learning (TT-HF) with cooperative D2D model aggregations.
result Achieves sublinear convergence rate of O(1/t) with adaptive control algorithm.
New learning rate approach reveals phase transitions in SGD performance.
problem Understanding feature learning dynamics in neural networks.
method Characterizing the relationship between learning rate(s) and sample complexity for gradient-based algorithms.
result Phase transition from information exponent to generative exponent regime with different learning rates.
New analysis shows how cross-entropy training shapes attention in transformers.
problem Understanding how gradient-based learning creates the required internal geometry in transformers.
method Developed a first-order analysis of cross-entropy training effects on attention scores and values in a transformer attention head.
result Introduced an advantage-based routing law and responsibility-weighted update for attention scores and values, respectively.