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…
Weak base-point freeness leads to Kähler-Ricci flow diameter bounds.
problem Bounding the diameter of Kähler-Ricci flow singularities.
method Weak transcendental base-point freeness on Kähler manifolds.
result Diameter lower bound for Kähler-Ricci flow singularities.
Finite-time bounds on error for linear stochastic approximation and TD learning.
problem Finite-time bounds on error for linear stochastic approximation and TD learning.
method Finite-time bounds derived using Lyapunov functions and Stein's method.
result Finite-time bounds on the moments of the error, including lower-order and higher-order moments.
In the context of an incomplete market with a Brownian filtration and a fixed finite time horizon, this paper proves that for general dynamic convex risk measures, the buyer's and seller's risk indifference prices of a contingent claim are bounded from below and above by the dynamic lower and upper hedging prices, resp…
Optimal strategy found for constrained multi-armed bandit problems.
problem Constrained multi-armed bandit problems.
method Extended ε_t-greedy strategy with asymptotic optimality.
result Asymptotic optimality achieved with a simple strategy.
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.
New bounds for Bayesian bandits show prior improves performance.
problem Improving regret bounds for Bayesian bandits.
method Upper confidence bound algorithm with finite-time logarithmic regret bounds.
result Derives O(cΔlogn) and O(chlog2n) upper bounds for Bayesian bandits. 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). 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…
We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action i, the learner receives information about the payoff of every action j in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair (i,j) (and may…
Paper proposes new γ-regret measure for non-episodic RL.
problem Measuring performance in non-episodic RL environments.
method Introduces γ-regret as a new performance measure and derives bounds. result Closed the gap between lower and upper bounds for γ-regret. 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.
Instead of investigating the Willmore flow for two-dimensional, closed immersed surfaces directly we turn to its inversion. We give a lower bound on the lifespan of this inverse Willmore flow, depending on the concentration of curvature in space and the extension of the initial surface, as well as a characterization of…
New algorithm adapts to unknown smoothness in stochastic bandits with polynomial cost.
problem Adapting to unknown smoothness in stochastic bandits.
method Reconsidered Locatelli and Carpentier's lower bound, defined admissible rate functions, and developed a new algorithm.
result New algorithm matches minimal rate functions and provides polynomial cost of adaptation.
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…
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.
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.
Proves Ricci flow extensibility with integral norms.
problem Ricci flow singularities under integral norms.
method Bounded integral norms of curvature and scalar curvature.
result Extends Ricci flow under certain conditions.
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.
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.
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.
Estimates Kähler metric diameters with entropy bound alone.
problem Estimating Kähler metric diameters.
method PDE techniques for L∞ estimates of the Monge-Ampère equation, improving degeneracies. result Diameter bounds for Kähler-Ricci flow and Calabi-Yau manifolds.
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…
This paper investigates stochastic and adversarial combinatorial multi-armed bandit problems. In the stochastic setting under semi-bandit feedback, we derive a problem-specific regret lower bound, and discuss its scaling with the dimension of the decision space. We propose ESCB, an algorithm that efficiently exploits t…
Study shows moment explosion time is finite for rough Heston model under certain conditions.
problem Understanding moment explosion times in the rough Heston model.
method Established upper and lower bounds, computed explosion time algorithm, analyzed critical moments.
result Finite critical moments for all maturities and negative correlation cases.
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.
This paper approximates SA iterates using Gaussian distributions for tail bounds.
problem Characterizing the distribution of stochastic approximation iterates in finite time.
method Approximating pre-limit distributions of SA iterates by Gaussian sequences with recursively defined covariances.
result Explicit bounds on the Wasserstein-1 distance between rescaled iterates and Gaussians.
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 optimal consumption and investment strategies with constraints in a market with random coefficients.
problem Optimal consumption and investment strategies with constraints in a regime switching market with random coefficients.
method Explicit optimal strategies provided via solutions to new BSDE systems.
result Solving new BSDEs to find optimal values and strategies.
Develops a regression approach for solving MDPs with general state and action spaces.
problem Solving MDPs with large or infinite state and action spaces.
method Regression-based primal-dual martingale approach.
result Tight upper and lower approximations of value functions and optimal policies.
A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametr…
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.
We study finite-time collapsing limits of the continuity method. When the continuity method starting from a rational initial Kähler metric on a projective manifold encounters a finite-time volume collapsing, this projective manifold admits a Fano fibration over a lower dimensional base. In this case, we prove the conti…
New study confirms some mean curvature flow solutions have bounded mean curvature.
problem Existence of mean curvature flow singularities with bounded mean curvature.
method Construction of specific solutions in RN for N≥8. result A nontrivial subset of solutions has uniformly bounded mean curvature.
Improved reinforcement learning with adaptive learning rates.
problem Enhancing the convergence rate of reinforcement learning algorithms.
method Two time-scale linear stochastic approximation algorithms, using Lyapunov functions and adaptive learning rates.
result Adaptive learning rate scheme significantly improves convergence rate over fixed learning rates.
The paper studies Yang-Mills flow on special holonomy manifolds and proves curvature bounds.
problem Analyzing finite-time singularities in Yang-Mills flow on special holonomy manifolds.
method Developed Yang-Mills flow and found curvature bounds sufficient to rule out finite-time singularities.
result Proved infinite-time bubbling set calibrated by (n−4)-form. 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.
Logarithmic regret for continuous-time reinforcement learning.
problem Continuous-time Markov decision processes with unknown transition probabilities and holding times.
method Upper confidence reinforcement learning, mean holding time estimation, stochastic comparison of point processes.
result Logarithmic regret bound achieved in finite time.
New algorithm improves regression error bounds and accelerates performance for low noise.
problem Nonparametric least square regression in RKHS with optimal error bounds.
method Kernel Truncated Randomized Ridge Regression (KTRRR) with optimal generalization error bounds.
result Faster finite-time and asymptotic rates on low noise problems.
A new algorithm for better decision-making in recommendation systems.
problem Stochastic multi-armed bandit problem and cold start problem in recommender systems.
method Proposes Hellinger-UCB, a variant of UCB algorithm using squared Hellinger distance.
result Hellinger-UCB reaches the theoretical lower bound and outperforms other algorithms in practical applications.
Curve shortening flow converges to a point with entropy bound.
problem Analyzing the behavior of curves under shortening flow near singularities.
method Analyzes blow-up limits and uses entropy bounds to prove convergence.
result Initial curves with entropy bound converge to a round point in finite time.
Upper bound on index of rotationally symmetric self-shrinking tori.
problem Stability of singularities in mean curvature flow.
method Entropy functional and eigenvalue analysis.
result Upper bound on the index of rotationally symmetric self-shrinking tori.
New algorithms for risk-averse bandits minimize regret in finite time.
problem Minimizing regret in finite time for bandit problems.
method Proposes two algorithms for selecting the most probable arm with a good risk-return trade-off.
result Upper bound for the minimum number of experiments before commitment to guarantee a bound on regret.
Study task-guided exploration in linear dynamical systems, improving sample complexity.
problem Efficiently learning about an environment to complete a specific task.
method Proposed a computationally efficient experiment-design based exploration algorithm.
result Optimally explores the environment, collecting precise information needed to complete the task.
ECPv2 optimizes Lipschitz functions efficiently and scalably.
problem Global optimization of Lipschitz-continuous functions with unknown Lipschitz constants.
method Adapting the Every Call is Precious (ECP) framework, ECPv2 introduces adaptive lower bounds, Worst-m memory, and random projections to reduce computational cost and improve acceptance regions.
result ECPv2 retains ECP's no-regret guarantees with optimal finite-time bounds and expands the acceptance region with high probability.
Asymptotically optimal algorithm for contextual linear bandits.
problem Contextual linear bandits with suboptimal algorithms.
method Decoupling context distribution and exploration policy, incremental primal-dual approach, confidence intervals.
result Asymptotic optimality and scalability of the algorithm.
Flexible algorithms for maximizing rewards in structured bandits.
problem Reward maximization in structured stochastic multi-armed bandit problems.
method Asymptotically optimal algorithms using iterative saddle-point solvers.
result Achieves optimal performance with minimal computational burden.