Cyclic coordinate descent identifies models in finite time and converges linearly.
problem Model identification in composite nonsmooth optimization problems.
method Cyclic coordinate descent for a wide class of functions.
result Explicit local linear convergence rates for coordinate descent.
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.
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.
Efficiently identifies best policies in tabular MDPs with reduced computational cost.
problem Identifying the best policy in tabular MDPs with high computational cost.
method Combines posterior sampling with online learning to achieve asymptotic optimality.
result Achieves optimal sample complexity and posterior contraction rate with O(S2AH) per episode. A distributed system identification method for LTI systems using reverse experience replay.
problem Online system identification of LTI systems over multi-agent networks.
method DSGD-RER, a distributed variant of SGD-RER with backward updates.
result The estimation error decreases as the network size grows.
Active learning method estimates nonlinear systems efficiently.
problem Identifying nonlinear dynamical systems with continuous states and actions.
method Repeating three steps: trajectory planning, tracking, and re-estimation.
result Estimates nonlinear dynamical systems at a parametric rate.
We identify linear dynamical systems under convex constraints with fewer samples.
problem Identifying linear dynamical systems with prior structural information.
method Constrained least squares estimator with error bounds dependent on convex set size.
result Linear dynamical systems can be reliably estimated with fewer samples than unconstrained settings.
Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
Improved SGD bounds for machine learning models with Markovian noise.
problem Uniform high-probability bounds for SGD under PL condition with Markovian noise.
method Combining Poisson equation for Markovian noise and probabilistic induction for almost-sure bounds.
result Matching 1/k decay rate for expected suboptimality. We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman al…
The main challenge for adaptive regulation of linear-quadratic systems is the trade-off between identification and control. An adaptive policy needs to address both the estimation of unknown dynamics parameters (exploration), as well as the regulation of the underlying system (exploitation). To this end, optimism-based…
AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.
problem Adaptive control in partially observable linear dynamical systems.
method AdaptOn algorithm that estimates system dynamics through online learning and gradient descent.
result AdaptOn achieves a logarithmic regret bound of polylog(T) after T steps.
New continuous-time optimization algorithms converge in finite time to local minima.
problem Finding local minima in optimization problems.
method Discontinuous dynamical systems with finite-time convergence via Lyapunov-based differential inequality.
result Finite-time convergence to strict local minima with provable settling time.
We study the problem of finding the optimal dosage in early stage clinical trials through the multi-armed bandit lens. We advocate the use of the Thompson Sampling principle, a flexible algorithm that can accommodate different types of monotonicity assumptions on the toxicity and efficacy of the doses. For the simplest…
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.
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…
Algorithm identifies best arm in combinatorial bandits with semi-bandit feedback.
problem Identifying the best arm in combinatorial bandits with semi-bandit feedback.
method Interpreted as a sequential zero-sum game, developed a CombGame meta-algorithm with finite time guarantees.
result First computationally efficient algorithm that is asymptotically optimal and has competitive empirical performance.
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.
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.
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.
The paper tackles joint learning of linear systems, improving accuracy with pooled data.
problem Estimating transition matrices of multiple related linear systems more accurately.
method Developed novel techniques to bound estimation errors and establish high probability bounds for singular values.
result Significant gains in accuracy achieved by pooling data across systems.
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…
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time versi…
New approach incentivizes strategic agents to explore, making exploration almost free.
problem Incentivized exploration in multi-armed bandits with long-term strategic agents.
method Simple incentive-provision strategy, best arm identification algorithm, and UCB lower bound.
result Exploration can be (almost) free when there are many learning agents.
Study of deep neural networks using finite-time Lyapunov exponents.
problem Understanding the geometric structures in input space formed by deep neural networks.
method Analogy with dynamical systems, computing finite-time Lyapunov exponents.
result Ridges of large positive exponents divide input space into regions associated with different classes.
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.
Algorithm optimally estimates linear dynamical systems with active input selection.
problem Estimating parameters of linear dynamical systems efficiently.
method Active learning with adaptive input selection.
result Finite time bound and asymptotic optimality proven.
In this note we study finite-time singularities in the Chern-Ricci flow. We show that finite-time singularities are characterized by the blow-up of the scalar curvature of the Chern connection.
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. In this short paper, we show that Kähler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.
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.
Paper analyzes finite-time performance of SA in RL with Markovian noise.
problem Finite-time analysis of linear two-timescale stochastic approximation with Markovian noise.
method Finite-time analysis of linear two-timescale SA with Markovian noise, considering both transient and steady-state terms.
result No discrepancy in convergence rate between Markovian and martingale noise; transient term is o(1/kc) and steady-state term is O(1/k). Compact curve solution emerges from non-compact curve.
problem Constructing solutions from non-compact curves.
method Slingshot solution to curve shortening flow.
result Compact embedded solution exists for a finite time.
Efficiently controls unknown linear systems with black-box interactions.
problem Controlling an unknown linear dynamical system from black-box interactions.
method First efficient algorithm with sublinear regret, using robust system identification.
result Resolves open problem on stochastic LQR and black-box LQR control.
Ricci flow singularities on compact Kähler surfaces are of Type I.
problem Understanding finite time singularities of Ricci flow on compact Kähler surfaces.
method Analyzing the Type I property of singularities.
result Non-collapsed finite time singularities are of Type I.
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-cocoercive games and develops adaptive algorithms. result Adaptive algorithms achieve same convergence rates as non-adaptive counterparts.
Finite-time extinction and smoothing effects in fractional fast diffusion on manifolds.
problem Finite-time extinction and smoothing effects in fractional fast diffusion equations.
method Nonlinear semigroups techniques, weighted Lp spaces, fractional Green function. result Sharp extinction rates and pointwise lower bounds for solutions.
This paper provides a set of sensitivity analysis and activity identification results for a class of convex functions with a strong geometric structure, that we coined "mirror-stratifiable". These functions are such that there is a bijection between a primal and a dual stratification of the space into partitioning sets…
Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.
problem Optimal stopping problems with finite-time horizon and state-dependent discounting.
method Linear diffusion process, time-homogeneous gain function, fine regularity properties, continuity and strict monotonicity proof.
result Proves continuity and strict monotonicity of the optimal stopping boundary under mild assumptions.
Given any embedded Lagrangian on a four dimensional compact Calabi-Yau, we find another Lagrangian in the same Hamiltonian isotopy class which develops a finite time singularity under mean curvature flow. This contradicts a weaker version of the Thomas-Yau conjecture regarding long time existence and convergence of Lag…
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…
We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data) subject to a network regularization term that penalizes a local model that differs fr…
The Kähler-Ricci flow's singularities are analyzed with bounds and convergence results.
problem Understanding the singularities and behavior of the Kähler-Ricci flow.
method Li-Yau type and Harnack estimates for weighted Ricci potential functions.
result Finite time singularities are shown to sub-converge to ancient solutions on analytic normal varieties.
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.
Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.
problem Queue peak laws in stochastic networks with geometric thresholds.
method Self-normalization mechanism
result Logarithmic scaling of queue peaks after geometric thresholds.
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.
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.