The paper analyzes deep neural networks using control theory to set a time limit for their convergence.
problem Understanding the finite-time convergence of deep neural networks.
method Lyapunov based analysis of the loss function, control theory framework, finite-time control of non-linear systems.
result A priori guarantees of finite-time convergence for deep neural networks are provided.
Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.
problem Analyzing stochastic approximation under heavy-tailed and LRD noise.
method Noise-averaging argument to regularize impact of non-classical noise.
result Established first finite-time moment bounds for SA under heavy-tailed and LRD noise.
Estimates for VPMCF show ancient MCF solutions and finite-time behavior.
problem Volume Preserving Mean Curvature Flow (VPMCF) behavior and singularities.
method Nonlocal estimates and blowup analysis.
result Ancient solutions to MCF and finite-time behavior of VPMCF.
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.
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…
The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.
problem Analyzing finite-time singularities in Spin(7)-structure flows.
method Proves Shi-type derivative estimates and shows that Λ(x,t) must blow up at finite-time singularities.
result Establishes a general analytic framework for studying Spin(7)-structure flows.
First-order method solves stochastic bilevel optimization with linear constraints.
problem Stochastic bilevel optimization with linear constraints and noise.
method Developed a novel framework using gradient-based techniques and smoothed penalty functions.
result Achieved finite-time convergence guarantees for (δ,ε)-Goldstein stationary points. 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) convergence rate in expectation and with high probability. The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower boun…
Paper analyzes finite-time guarantees for preference-based RL.
problem Understanding finite-time guarantees for preference-based RL.
method Combines dueling bandits and policy search to navigate state space.
result Identifies best policy up to accuracy ε with high probability.
New bounds derived for KG algorithm's performance in finite time.
problem Best arm identification problem in multi-armed bandit.
method Theoretical analysis of finite-time performance, deriving bounds for sample allocation, error probability, and regret.
result Upper and lower bounds for the probability of error and simple regret of the KG algorithm.
I introduce and analyse an anytime version of the Optimally Confident UCB (OCUCB) algorithm designed for minimising the cumulative regret in finite-armed stochastic bandits with subgaussian noise. The new algorithm is simple, intuitive (in hindsight) and comes with the strongest finite-time regret guarantees for a hori…
I analyse the frequentist regret of the famous Gittins index strategy for multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it turns out that this approach leads to finite-time regret guarantees comparable to those available for the popular UCB algorithm. Along the way I derive finite-time bounds…
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…
New analysis shows actor-critic method converges efficiently in practical settings.
problem Understanding finite-time convergence of single-timescale actor-critic methods.
method Investigated online single-timescale actor-critic algorithm with linear function approximation and Markovian sampling.
result Proved convergence to ε-approximate stationary point with sample complexity of O(ε^(-2)).
This work analyzes actor-critic methods for faster convergence.
problem Finite-time analysis and sample complexity of two-time-scale actor-critic methods.
method Non-asymptotic analysis under non-i.i.d. setting, proving convergence to first-order stationary point.
result Actor-critic method finds a first-order stationary point with ildeO(ε−2.5) sample complexity. New analysis of stochastic approximation with non-expansive mappings.
problem Finite-time analysis of two-time-scale stochastic approximation with non-expansive mappings.
method Studied two-time-scale stochastic approximation algorithms with non-expansive mappings and projection steps.
result Last-iterate mean square residual error decays at a rate O(1/k1/4−ε). Constructing eigenfunctions for finite-time singularities in Lagrangian mean curvature flow
problem Constructing eigenfunctions for finite-time singularities in Lagrangian mean curvature flow
method Constructing eigenfunctions for finite-time singularities in Lagrangian mean curvature flow
result Identifying the lowest eigenfunction with the scaling mode of the special Lagrangian desingularization
Paper analyzes NAC with neural networks for efficient policy optimization.
problem Improving sample and iteration complexity in policy optimization.
method Entropy regularization, averaging, neural network approximation, and optimization techniques.
result Entropy regularization and averaging ensure stability and sharp sample complexity bounds.
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
problem Achieving decoupled convergence in nonlinear two-time-scale stochastic approximation.
method Nested local linearity assumption, suitable step size selection, convergence analysis of matrix cross term, fourth-order moment convergence rates.
result Finite-time decoupled convergence rates can be achieved in nonlinear two-time-scale stochastic approximation with proper step size selection.
Paper analyzes convergence of dynamic policy gradient for MDPs, improving performance in finite-time problems.
problem Optimal policies in finite-time MDPs are not stationary and require epoch-specific training.
method Introduces dynamic policy gradient combining dynamic programming and policy gradient, analyzes convergence for softmax parametrisation.
result Dynamic policy gradient training exploits finite-time structure, leading to better convergence bounds.
Theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
problem Lack of precise theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
method Adapting a finite-time convergence analysis to the asymmetric actor-critic setting with linear function approximators.
result A finite-time bound reveals that the asymmetric critic eliminates aliasing errors in the agent state.
We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an associated ordinary differential equation (ODE). We obtain finite-time bounds on t…
Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.
problem Optimizing control actions in unknown continuous-time systems over a finite time horizon.
method Least-squares algorithm based on continuous-time observations and controls, with perturbation analysis and parameter estimation error analysis.
result Logarithmic regret bound of order O((lnM)(lnlnM)). The OLS estimator optimally identifies stable linear systems with a finite number of samples.
problem Identifying stable linear systems with a finite number of samples.
method Finite-time analysis of the Ordinary Least Squares (OLS) estimator for stable linear systems.
result The OLS estimator achieves optimal sample complexity for stable systems, matching existing lower bounds up to universal factors.
Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement learning, its theoretical analysis has proved challenging and few guarantees on its s…
New Thompson sampling algorithm reduces regret for exponential family bandits.
problem Minimizing regret in multi-armed bandit problems with exponential family rewards.
method Proposes ExpTS and ExpTS+ algorithms using novel sampling distributions. result Minimizes both finite-time and asymptotic regret for exponential family rewards.
The paper offers precise bounds for averaged LSA iterates in linear systems.
problem Computing approximate solutions of linear systems with noisy observations.
method Finite-time analysis of LSA algorithms with Polyak-Ruppert averaging.
result Sharp high-probability bounds for averaged LSA iterates.
Constructs finite-time singularities in Lagrangian mean curvature flow with precise dynamics.
problem Finite-time singularities in Lagrangian mean curvature flow.
method Modulation analysis around shrinking cohomogeneity-one special Lagrangian desingularizations.
result Explicit curvature blow-up rate and precise dynamics of singularities.
Proposes a TS approach for Bayesian optimization with preferential feedback.
problem Optimizing with preference feedback in complex applications.
method Uses Thompson Sampling with a dueling kernel and anchor invariance.
result Performance matches standard TS for scalar feedback in finite time.
This work analyzes Q-learning with adaptive stepsizes for finite-time convergence.
problem Finite-time convergence analysis for average-reward 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 ildeO(1/k) for mean-square and pointwise mean-square convergence. Paper analyzes SVGD algorithm for non-asymptotic convergence.
problem Optimizing a set of particles to approximate a target probability distribution.
method Finite time analysis of SVGD algorithm, providing descent lemma and convergence rates.
result SVGD algorithm decreases the objective at each iteration and converges to the target distribution.
We study an extension of the classic stochastic multi-armed bandit problem which involves multiple plays and Markovian rewards in the rested bandits setting. In order to tackle this problem we consider an adaptive allocation rule which at each stage combines the information from the sample means of all the arms, with t…
We tackle the problem of online reward maximisation over a large finite set of actions described by their contexts. We focus on the case when the number of actions is too big to sample all of them even once. However we assume that we have access to the similarities between actions' contexts and that the expected reward…
It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.
In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based differential inequality for differential inclusions, which leads to finite-time …
Minimal assumptions analysis of Q-learning with time-varying policies.
problem Finite-time analysis of Q-learning with time-varying policies for discounted MDPs.
method Minimal assumptions, Poisson equation decomposition, sensitivity analysis.
result Established convergence rate and sample complexity for Q-learning.
Study finite time singularities in Ricci flow with bounded scalar curvature.
problem Understanding finite time singularities in Ricci flow with bounded scalar curvature.
method Analyzing blow-up sequences of locally Type I singularities.
result Every blow-up sequence of a locally Type I singularity has a specific property.
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.
Single-timescale analysis improves convergence in multi-sequence stochastic approximation.
problem Finite-time convergence of nonlinear stochastic approximation with multiple coupled sequences.
method Smoothness property of fixed points and analysis of fine-grained single-timescale SA.
result Improved iteration complexity for achieving ε-accuracy in multi-sequence single-timescale SA.
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/n2/3) and O(1/n) under different conditions. Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild "ergodic-like" assumption on the underlying stochastic noise sequence. Building upon a carefully designed multistep…
New scalable MARL framework for dynamic networked systems.
problem Scalability in multi-agent reinforcement learning with dynamic dependencies.
method Scalable Actor Critic framework for non-local and stochastic dependencies.
result Finite-time error bound showing convergence rate dependence on information spread speed.
Finite-time blow-up in Yang-Mills flow for small energy initial connections.
problem Finite-time blow-up of Yang-Mills flow solutions.
method Analyzing the Yang-Mills flow on Riemannian and Kähler manifolds.
result Finite-time blow-up occurs for small energy initial connections.
Unified analysis of stochastic iterative algorithms using Lyapunov functions.
problem Analyzing convergence of stochastic iterative algorithms for fixed-point equations.
method Lyapunov-based techniques for finite-time analysis of stochastic approximation algorithms.
result Unified mean-square convergence guarantees for various algorithms.
Optimizes stochastic linear bandits with efficient, asymptotically optimal algorithm.
problem Optimizing stochastic linear bandits with multiple actions.
method Frequentist information-directed sampling (IDS) with a surrogate for information gain.
result Asymptotically optimal and nearly worst-case optimal in finite time.
We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first…
We consider the question of whether solutions of variants of Teichmüller harmonic map flow from surfaces M to general targets can degenerate in finite time. For the original flow from closed surfaces of genus at least 2, as well as the flow from cylinders, we prove that such a finite-time degeneration must occur in…