Paper proposes a sequential statistical test for comparing imitation learning policies with near-optimal stopping.
problem Challenges in rigorously comparing imitation learning policies due to small sample sizes and potential p-hacking.
method Sequential statistical test that adapts the number of trials based on intermediate results, achieving near-optimal stopping.
result Reduces the number of evaluation trials by up to 32% compared to state-of-the-art baselines, saving significant time and effort.
Near-optimal confidence intervals for bounded data.
problem Online inference for sequential decision problems like A/B testing.
method Utilizing Bentkus' concentration results to improve on existing methods.
result Near-optimal confidence intervals confirmed favorable in synthetic and practical applications.
New algorithm solves complex stopping problems with robust optimization.
problem Solving complex stochastic optimal stopping problems.
method Simulation-based robust optimization with exact reformulation as a zero-one bilinear program.
result Developed polynomial-time heuristics and algorithms for practical solution.
Develops first optimal algorithm for logistic bandits.
problem Pure exploration in logistic bandits.
method Logistic track-and-stop (Log-TS) algorithm.
result Asymptotically matches lower bound for expected sample complexity.
Depth is a key component of Deep Neural Networks (DNNs), however, designing depth is heuristic and requires many human efforts. We propose AutoGrow to automate depth discovery in DNNs: starting from a shallow seed architecture, AutoGrow grows new layers if the growth improves the accuracy; otherwise, stops growing and …
This study analyzes AdaGrad's stability and convergence in non-convex optimization.
problem Lack of theoretical analysis for AdaGrad in non-convex optimization.
method Novel stopping time-based techniques from probability theory.
result Established stability and derived convergence rates for AdaGrad.
Transforms any test into anytime-valid with sample savings.
problem Sequential data invalidates classical test guarantees.
method Predicts test outcomes to create anytime-valid stopping rules.
result Ensures Type-I error control and near-optimal power.
We consider the problem where an agent wants to find a hidden object that is randomly located in some vertex of a directed acyclic graph (DAG) according to a fixed but possibly unknown distribution. The agent can only examine vertices whose in-neighbors have already been examined. In this paper, we address a learning s…
Near-optimal tests and confidence sequences for non-parametric data.
problem Flexible statistical inference and decision-making with non-parametric data.
method Classic delayed-start normal-mixture sequential probability ratio tests with asymptotic guarantees.
result Asymptotically optimal type-I error and expected rejection time guarantees.
In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the und…
DP-SPRT improves privacy in sequential tests with near-optimal error rates.
problem Privacy constraints in sequential probability ratio tests.
method A wrapper for SPRT that uses a private mechanism to determine when to stop based on predefined intervals.
result DP-SPRT achieves near-optimal error rates and privacy guarantees.
Q-learning with function approximation is one of the most popular methods in reinforcement learning. Though the idea of using function approximation was proposed at least 60 years ago, even in the simplest setup, i.e, approximating Q-functions with linear functions, it is still an open problem on how to design a pr…
New method learns BN structures from data efficiently.
problem Learning sparse DAG structure of BN from continuous data.
method Consistent second-order conic integer programming with early stopping criterion.
result Near-optimal solutions to medium-size problems within reasonable time.
Solves optimal stopping problem with Poisson constraints using jumps.
problem Optimal stopping with Poisson constraints and jumps.
method Penalized backward stochastic differential equation (PBSDE) with jumps, decomposition method based on Jacod-Pham, comparison theorem of BSDEs with jumps.
result Solves American option pricing in nonlinear markets with Poisson constraints.
Neural networks optimize stopping boundaries in financial instruments.
problem Optimizing stopping boundaries in financial instruments.
method Deep neural networks and empirical risk minimization for parameterizing stopping boundaries.
result Proved existence of stopping boundary under natural assumptions.
New method stops experiments early for harm in diverse groups.
problem Early stopping of experiments for harmful treatment effects in diverse populations.
method Causal machine learning approach (CLASH) for early stopping.
result CLASH effectively stops experiments early for harmful treatment effects in diverse groups.
A survey of existing methods for stopping active learning (AL) reveals the needs for methods that are: more widely applicable; more aggressive in saving annotations; and more stable across changing datasets. A new method for stopping AL based on stabilizing predictions is presented that addresses these needs. Furthermo…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …
DO-IQS recovers optimal stopping region from expert trajectories, addressing specific challenges.
problem Recovering optimal stopping region from expert trajectories with unknown gain functions.
method Dynamics-Aware Offline Inverse Q-Learning incorporating temporal information and confidence-based oversampling.
result Demonstrated performance on real and artificial data, including optimal intervention for critical events.
The paper tackles optimal stopping problems using reinforcement learning and singular control.
problem Continuous-time and state-space optimal stopping problems.
method Formulated as a singular control problem with randomized stopping times and penalized cumulative residual entropy.
result Identified unique optimal exploratory strategy through dynamic programming.
The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy for a form of gradient-descent applied to the least-squares loss function. We pro…
Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
problem Optimal stopping problem of a Gauss-Markov bridge.
method Time-space transformation approach, Picard iteration algorithm.
result Lipschitz continuity of the optimal stopping boundary and its characterization.
New algorithms improve stopping time for best arm identification.
problem Efficiently identifying the best alternative in experiments.
method Proposed algorithms with exponential-tailed stopping time.
result Proved that some algorithms never stop, leading to new methods.
NeAda solves nonconvex minimax optimization by balancing primal and dual variables adaptively.
problem Nonconvex minimax optimization challenges with parameter-agnostic adaptive algorithms.
method Nested Adaptive (NeAda) framework with inner and outer loops for primal and dual variables.
result Achieves near-optimal convergence rates for nonconvex-strongly-concave problems.
Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject to a trailing stop. Under a general linear diffusion framework, we study an opt…
Continuous-time optimal stopping solved with deep reinforcement learning
problem Optimal stopping problems in continuous time
method CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping)
result Higher prices than existing Bermudan solvers, approaching American upper bound
Study proposes a stopping criterion for active learning based on error stability.
problem Improving predictive performance in active learning by adaptively annotating samples.
method Proposes a stopping criterion based on error stability for Bayesian active learning.
result Demonstrates the proposed criterion stops active learning at the appropriate timing for various models and datasets.
Dual martingales improve primal optimal stopping problem efficiency.
problem Optimal stopping problem in the primal formulation.
method Investigation of dual martingales to improve primal methods.
result Accurate dual martingale approximations reduce primal problem variance.
We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…
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.
Early stopping improves logistic regression's calibration and consistency in high dimensions.
problem Improving the statistical performance of gradient descent in overparameterized logistic regression.
method Investigates the effects of early stopping on gradient descent in logistic regression.
result Early-stopped gradient descent is well-calibrated and statistically consistent, while asymptotic gradient descent is not.
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit …
Early stopping improves sample quality in latent diffusion models.
problem Latent diffusion models degrade sample quality with conventional early stopping.
method Analyzed the interaction between latent dimension and stopping time under Gaussian framework.
result Lower-dimensional representations benefit from earlier termination, higher-dimensional spaces require later stopping.
In this paper, we propose an adaptive stopping rule for kernel-based gradient descent (KGD) algorithms. We introduce the empirical effective dimension to quantify the increments of iterations in KGD and derive an implementable early stopping strategy. We analyze the performance of the adaptive stopping rule in the fram…
Paper solves a complex stopping problem using regularization and HJB equations.
problem Time-inconsistent mean-variance optimal stopping problem
method Vanishing regularization method to derive HJB equations and prove existence of solutions
result Formally recovers variational inequalities for original problem
Criterion for stopping conjugacy class enumeration in triangle groups.
problem Enumerating all conjugacy classes in cocompact triangle groups.
method Encoding by P. Dehornoy and T. Pinsky; stopping criterion based on geometric length.
result Stopping criterion for the generation of conjugacy classes in cocompact triangle groups.
The paper studies early stopping methods in linear contextual bandits.
problem Minimizing in-experiment regret and conducting robust post-experiment inferences in contextual bandits.
method The study proposes early stopping rules based on the Opportunity Cost and Threshold Method, using variances of estimators to quantify upper regret bounds.
result The proposed method provides a systematic approach to minimize in-experiment regret and conduct robust post-experiment inferences.
MUSE provides unbiased stopping estimates for optimal problems.
problem Estimating the utility of optimal stopping problems.
method Backward recursive construction of the Multilevel Unbiased Stopping Estimator (MUSE).
result MUSE achieves ε-accuracy with O(1/ε^2) computational cost.
Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by the overarching goal in finance to maximize expected returns given available infor…
The study reveals optimal early stopping behaviors in deep learning models.
problem Understanding optimal early stopping in deep learning models.
method Theoretical analysis of linear models and experimental validation.
result Two distinct behaviors of optimal early stopping time depending on model dimension relative to dataset features.
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
This paper improves neural network predictions with early stopping using conformal calibration.
problem Lack of precise statistical guarantees for neural networks trained with early stopping.
method Conformalized early stopping that combines early stopping with conformal calibration.
result Models provide both accuracy and precise inferences without additional data splits.
Study optimal stopping in random exploration, deriving HJB and designing a reinforcement learning algorithm.
problem Optimal stopping problem in continuous time with random exploration.
method Transformed optimal stopping to optimal control problem, derived HJB equation, designed reinforcement learning algorithm.
result Convergence rate of policy iteration and comparison to classical optimal stopping.
Study optimal stopping times under regime-switching models with constraints.
problem Optimal stopping times for discounted payoffs on a regime-switching geometric Brownian motion.
method Solve variational inequality to find value functions and optimal thresholds.
result Existence and expressions of optimal stopping times under specific conditions.
We consider the optimal double stopping time problem defined for each stopping time S by $v(S)=\esssup\{E[ψ(τ_1, τ_2) | \F_S], τ_1, τ_2 \geq S \}$. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of …
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The op…
We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time…
This work bounds the run-time of nonconvex optimization with early stopping.
problem Bounding the expected run-time of nonconvex optimization with early stopping.
method Derives conditions for well-defined early stopping based on validation function norms and bounds the expected number of iterations and gradient evaluations.
result Guarantees the validity of early stopping and provides bounds on the expected run-time for various optimization algorithms.